BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Yan Soibelman (Kansas State University)
DTSTART:20200416T203000Z
DTEND:20200416T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/1
DESCRIPTION:Title: Holomorphic Floer theory and deformation quantization\nby Yan Soibel
man (Kansas State University) as part of M-seminar\n\n\nAbstract\nIn his 2
1st problem Hilbert asked about reconstruction of Fuchsian differential eq
uation from its monodromy. This Riemann-Hilbert problem has a long history
of solutions and counterexamples. During last decades it was generalized
in two different directions. Most well-known is the generalization to high
er dimensions and D-modules\, with possibly irregular singularities. The m
onodromy data are replaced by constructble sheaves. Another\, less known\,
generalization deals with not necessarily differential equations\, e.g.
with difference of q-difference ones.\n\nIn 2014 together with Maxim Konts
evich we started a project on what we called Holomorphic Floer theory. The
word "holomorphic" refers to the fact that we consider Floer theory (e.g
. Fukaya categories) for comlex symplectic manifolds. Aim of my talk is to
explain some parts of the project which lead to a general formulation of
the Riemann-Hilbert correspondence as a relation between Floer theory and
deformation quantization.\n
LOCATION:https://researchseminars.org/talk/M-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Cheltsov (University of Edinburgh)
DTSTART:20200430T193000Z
DTEND:20200430T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/2
DESCRIPTION:Title: K-stability of Fano 3-folds\nby Ivan Cheltsov (University of Edinbur
gh) as part of M-seminar\n\n\nAbstract\nA smooth Fano manifold admits a Ka
hler-Einstein metric if and only if it is K-polystable (K-stable if the au
tomorphism group is finite). In this talk\, I will explain how to prove an
d disprove K-polystability and K-stability using basic tools of birational
geometry. The talk will will be focused on smooth Fano threefolds. This i
s a joint group project with Carolina Araujo\, Ana-Maria Castravet\, Kento
Fujita\, Anne-Sophie Kaloghiros\, Jesus Martinez-Garcia\, Constantin Shra
mov\, Hendrick S\\"u\\ss\, and Nivedita Viswanathan.\n
LOCATION:https://researchseminars.org/talk/M-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peng Zhou (UC Berkeley)
DTSTART:20200423T203000Z
DTEND:20200423T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/3
DESCRIPTION:Title: Variation of toric GIT quotient and variation of Lagrangian skeleton
\nby Peng Zhou (UC Berkeley) as part of M-seminar\n\n\nAbstract\nIt is wel
l-known that the GIT quotient depends on a choice of an equivariant ample
line bundle. Various different quotients are related by birational transfo
rmations\, and their B-models (D^bCoh) are related by semi-orthogonal deco
mpositions\, or derived equivalences. If we apply mirror symmetry\, it is
natural to ask how the A-models of the mirror of various quotients are rel
ated. We give a description in the case of toric variety\, where the A-sid
e is described using constructible sheaves and Lagrangian skeleton.\n
LOCATION:https://researchseminars.org/talk/M-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Kerr (Kansas State University)
DTSTART:20200507T203000Z
DTEND:20200507T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/4
DESCRIPTION:Title: Phase tropical hypersurfaces\nby Gabriel Kerr (Kansas State Universi
ty) as part of M-seminar\n\n\nAbstract\nIn this talk\, I will give the def
inition of the phase tropical hypersurface arising from a polytope with a
coherent triangulation. This is a topological version of a singular integr
able system. I will discuss aspects of a joint work with I. Zharkov which
proved that there is a homeomorphism between the phase tropical hypersurf
ace and a complex hypersurface (this is known as Viro's Conjecture). With
this\, Mikhalkin's pair of pants decomposition of a complex hypersurface b
ecomes a polyhedral decomposition and several Lagrangians arising in mirro
r symmetry have conjectural accompanying decompositions which are well con
trolled topologically. I will discuss these subcomplexes and evidence of t
heir mirrors in matrix factorizations. This is joint work with I. Zharkov.
\n
LOCATION:https://researchseminars.org/talk/M-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Diaconescu (Rutgers University)
DTSTART:20200514T160000Z
DTEND:20200514T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/5
DESCRIPTION:Title: Mckay correspondence and cohomological Hall algebras\nby Emanuel Dia
conescu (Rutgers University) as part of M-seminar\n\n\nAbstract\nIt is sho
wn that derived McKay correspondence for type A Kleinian singularities ind
uces an isomorphism of cohomological Hall algebras associated to semistabl
e objects of fixed slope. Moreover\, these algebras are explicitely determ
ined in terms of Yangians associated to finite type A Dynkin quivers. This
is joint work with Mauro Porta and Francesco Sala.\n
LOCATION:https://researchseminars.org/talk/M-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Neitzke (Yale University)
DTSTART:20200521T203000Z
DTEND:20200521T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/6
DESCRIPTION:Title: Abelianization of flat connections\, and its q-deformation\nby Andre
w Neitzke (Yale University) as part of M-seminar\n\n\nAbstract\nAbelianiza
tion of flat connections is a construction motivated by supersymmetric qua
ntum field theory\, which has turned out to be connected to various bits o
f geometry -- in particular\, to Donaldson-Thomas theory\, cluster algebra
\, the exact WKB method for analysis of ODEs\, and hyperkahler geometry. I
n some of these subjects it is known that there exists a natural q-deforma
tion which takes us from the commutative to the noncommutative world. This
suggests that there ought to exist a q-deformation of abelianization as w
ell. I will explain joint work in progress with Fei Yan on constructing th
is q-deformation in a geometric way using spectral networks. This construc
tion is inspired by related work by various authors\, especially Bonahon-W
ong\, Gabella\, Gaiotto-Witten. One byproduct is a new scheme for computin
g known polynomial invariants of links in R^3\, which generalizes the usua
l "vertex models".\n
LOCATION:https://researchseminars.org/talk/M-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (Stanford University)
DTSTART:20200528T203000Z
DTEND:20200528T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/7
DESCRIPTION:Title: Non-archimedean mirrors of symplectic cluster manifolds in real dimensio
n four\nby Umut Varolgunes (Stanford University) as part of M-seminar\
n\n\nAbstract\nI will start by explaining what I mean by a symplectic clus
ter manifold focusing on how to represent them by certain combinatorial da
ta called an eigenray diagram (4d only!). These symplectic manifolds admit
a Lagrangian fibration over the real plane with only focus-focus singular
ities. They do not need to have convex boundary or exact symplectic form\,
but they are open and geometrically bounded. Eigenray diagrams are relate
d to toric models and the relation will be briefly mentioned. Then\, using
relative symplectic cohomology and a locality statement that relies on mo
notonicity techniques\, I will describe conjectural mirrors of symplectic
cluster manifolds as certain deformed (over the Novikov field) cluster var
ieties. This is joint work with Yoel Groman.\n
LOCATION:https://researchseminars.org/talk/M-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Negut (MIT)
DTSTART:20200604T190000Z
DTEND:20200604T200000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/8
DESCRIPTION:Title: A brief survey of 2D K-HAs\nby Andrei Negut (MIT) as part of M-semin
ar\n\n\nAbstract\nI will give an introduction into the study of an interes
ting class of algebraic structures\, namely K-theoretic Hall algebras of q
uivers and surfaces. The emphasis will be on computational tools\, such as
shuffle algebras and intersection theory\, and how to use them in order t
o obtain concrete applications to problems from geometry\, representation
theory and mathematical physics.\n
LOCATION:https://researchseminars.org/talk/M-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Pantev (University of Pennsylvania)
DTSTART:20200611T160000Z
DTEND:20200611T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/9
DESCRIPTION:Title: Enhanced moduli of D-branes and superpotentials\nby Tony Pantev (Uni
versity of Pennsylvania) as part of M-seminar\n\n\nAbstract\nModuli of D-b
ranes on to Calabi-Yau manifolds are naturally equipped with enhanced geom
etric structures which play important role in classical field theory and a
re an essential input for the quantization problem. I will explain how one
can recognize when such enhanced structures arise from a local or global
superpotential. I will discuss applications to higher dimensional Chern-Si
mons functionals\, to non-abelian Hodge theory\, to the moduli spaces of f
ramed sheaves on log Calabi-Yau geometries\, and to the moduli of monopole
s. This is based on joint works with Calaque\, Katzarkov\, Toen\, Vaquie\,
and Vezzosi.\n
LOCATION:https://researchseminars.org/talk/M-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (UC Berkeley)
DTSTART:20200618T203000Z
DTEND:20200618T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/10
DESCRIPTION:Title: Knot categorification and mirror symmetry\nby Mina Aganagic (UC Ber
keley) as part of M-seminar\n\n\nAbstract\nI will describe some aspects of
two geometric approaches to the knot categorification problem\, which fol
low from string theory. They provide new examples of homological mirror sy
mmetry and its equivariant generalization\, with deep relation to represen
tation theory.\n
LOCATION:https://researchseminars.org/talk/M-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dima Arinkin (University of Wisconsin-Madison)
DTSTART:20200625T180000Z
DTEND:20200625T190000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/11
DESCRIPTION:Title: Singular support of categories\nby Dima Arinkin (University of Wisc
onsin-Madison) as part of M-seminar\n\n\nAbstract\nIn many situations\, ge
ometric objects on a space have some kind of singular support\, which refi
nes the usual support. For instance\, for smooth X\, the singular support
of a D-module (or a perverse sheaf) on X is as a conical subset of the cot
angent bundle\; there is also a version of this notion for coherent sheave
s on local complete intersections. I would like to describe a higher categ
orical version of this notion. Let X be a smooth variety\, and let Z be a
closed conical isotropic subset of the cotangent bundle of X. I will defin
e a 2-category associated with Z\; its objects may be viewed as `categorie
s over X with singular support in Z'. In particular\, if Z is the zero sec
tion\, this gives the notion of categories over Z in the usual sense.The p
roject is motivated by the local geometric Langlands correspondence\; time
permitting\, I plan to sketch the relation with the Langlands corresponde
nce at the end of the talk.\n
LOCATION:https://researchseminars.org/talk/M-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina)
DTSTART:20200709T183000Z
DTEND:20200709T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/12
DESCRIPTION:Title: Elliptic stable envelopes and symplectic duality\nby Andrey Smirnov
(University of North Carolina) as part of M-seminar\n\n\nAbstract\nIn thi
s talk I'll explain the following idea: "the elliptic stable envelopes of
symplectic dual varieties coincide." I'll describe a simplest example of $
T^*P^1$ in details and discuss other cases in which the statement is prove
n.\n
LOCATION:https://researchseminars.org/talk/M-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20200716T203000Z
DTEND:20200716T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/13
DESCRIPTION:Title: Rozansky-Witten geometry of Coulomb branches\nby Sergei Gukov (Calt
ech) as part of M-seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/M-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHES)
DTSTART:20200702T183000Z
DTEND:20200702T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/14
DESCRIPTION:Title: On higher critical points in calculus of variations\nby Maxim Konts
evich (IHES) as part of M-seminar\n\n\nAbstract\nIn classical mechanics\,
the variational principle implies the existence of a canonical closed 2-fo
rm on the space of solutions of the Euler-Lagrange equation. I will explai
n an origin of this 2-form via coarse geometry\, and relation with the 1st
cohomology with compact support of the space-time. Then I'll introduce a
generalization to higher critical points. The basic example is higher Cher
n-Simons theory on 5-dimensional manifolds.\n
LOCATION:https://researchseminars.org/talk/M-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (UC Davis)
DTSTART:20200723T203000Z
DTEND:20200723T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/15
DESCRIPTION:Title: 3D Mirror Symmetry and HOMFLY-PT Homology\nby Tudor Dimofte (UC Dav
is) as part of M-seminar\n\n\nAbstract\nA recent construction of HOMFLY-PT
knot homology by Oblomkov-Rozansky has its physical origin in “B-twiste
d” 3D N=4 gauge theory\, with adjoint and fundamental matter. Mathematic
ally\, the construction uses certain categories of matrix factorization. W
e apply 3D Mirror Symmetry to identify an A-twisted mirror of this constru
ction. In the case of algebraic knots\, we find that knot homology on the
A side gets expressed as cohomology of affine Springer fibers (related but
not identical to work if Gorsky-Oblomkov-Rasmussen-Shende). More generall
y\, we propose a Fukaya-Seidel category mirror to the Oblomkov-Rozansky ma
trix factorization.\nJoint work with N Garner\, J Hilburn\, A Oblomkov\, a
nd L Rozansky.\n
LOCATION:https://researchseminars.org/talk/M-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Zaslow (Northwestern University)
DTSTART:20200730T203000Z
DTEND:20200730T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/16
DESCRIPTION:Title: A Diagrammatic Calculus for Legendrian Surfaces\nby Eric Zaslow (No
rthwestern University) as part of M-seminar\n\n\nAbstract\nI will describe
work with Roger Casals. We show how planar diagrams called N-graphs enco
de Legendrian surfaces which cover the plane N-to-1. These N-graphs can b
e used to express Reidemeister moves\, surgeries\, and connect sums\; to d
escribe a Markov move a` la braids\; to construct large classes of example
s of any genus\; to define moduli spaces which can be used to distinguish
surfaces up to Legendrian isotopy\; to discuss cluster charts and mutation
s\; to construct exact Lagrangian fillings\; and to define a planar algebr
a.\n
LOCATION:https://researchseminars.org/talk/M-seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Ekholm (Uppsala University)
DTSTART:20200806T180000Z
DTEND:20200806T190000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/17
DESCRIPTION:Title: Holomorphic curves on knot conormals\nby Tobias Ekholm (Uppsala Uni
versity) as part of M-seminar\n\n\nAbstract\nWe give an overview of result
s from the last few years. We first describe the "skeins on branes” appr
oach (joint with Shende) to open Gromov-Witten invariants and show how thi
s leads to a direct geometric interpretation of the quantization of the au
gmentation variety of a Legendrian knot conormal\, as a quantum curve. We
then describe a partially conjectural quiver picture (joint with Kucharski
and Longhi) for the holomorphic curve counts on a Lagrangian knot conorma
l\, where all curves stems from a finite set of basic holomorphic disks.
Via more refined disk counts\, this quiver picture leads to a description
of HOMFLY homology. Finally\, we apply similar reasoning to the knot compl
ement Lagrangian we find that a count of holomorphic annuli\, after SFT s
tretching\, can be viewed as the semi-classical limit of an instance of Gu
kov-Pei-Putrov-Vafa Z-hat theory. This leads to a direct geometric interpr
etation of the Z-hat invariant (joint with Guen\, Gukov\, Kucharski\, Park
\, and Sulkowski).\n
LOCATION:https://researchseminars.org/talk/M-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael McBreen (CUHK)
DTSTART:20200813T203000Z
DTEND:20200813T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/18
DESCRIPTION:Title: Symplectic duality and twisted quasimaps\nby Michael McBreen (CUHK)
as part of M-seminar\n\n\nAbstract\nHypertoric varieties are a hyperkahle
r analogue of toric varieties which arise frequently in geometric represen
tation theory. I will explain how the virtual count of twisted quasimaps t
o a hypertoric variety can be reformulated as a kind of trace on a periodi
zed symplectically dual hypertoric. Joint work with Artan Sheshmani and Sh
ing-Tung Yau.\n
LOCATION:https://researchseminars.org/talk/M-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiraku Nakajima (IPMU)
DTSTART:20200820T230000Z
DTEND:20200821T000000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/19
DESCRIPTION:Title: Bow varieties and representations of affine Lie algebras\nby Hiraku
Nakajima (IPMU) as part of M-seminar\n\n\nAbstract\nCherkis bow varieties
of affine type A are common generalization of quiver varieties and Coulom
b branches of affine type A. We construct commuting representations of aff
ine $sl_l$ and $sl_n$ on the direct sum of their homology groups (more pre
cisely homology groups of attracting sets)\, as common generalization of c
orresponding results for quiver varieties and geometric Satake for affine
$sl_n$. This is a part of a joint work in progress with Dinakar Muthiah.\n
LOCATION:https://researchseminars.org/talk/M-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pyongwon Suh (Northwestern University)
DTSTART:20200827T203000Z
DTEND:20200827T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/20
DESCRIPTION:Title: The coherent-constructible correspondence for toric projective bundles<
/a>\nby Pyongwon Suh (Northwestern University) as part of M-seminar\n\n\nA
bstract\nThis talk is about the coherent-constructible correspondence (CCC
). CCC is a version of homological mirror symmetry for toric varieties. It
equates the derived category of coherent sheaves on a toric variety and t
he category of constructible sheaves on a torus that satisfy some conditio
n on singular support. Recently\, Harder-Katzarkov conjectured that there
should be a version of CCC for toric fiber bundles and they proved their c
onjecture for $\\mathbb{P}^1$-bundles. I will explain how we can prove (ha
lf of) their conjecture for $\\mathbb{P}^n$-bundles. If time permits\, I w
ill give a more precise version of the conjecture for arbitrary toric fibe
r bundles.\n
LOCATION:https://researchseminars.org/talk/M-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Goncharov (Yale University)
DTSTART:20200903T203000Z
DTEND:20200903T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/21
DESCRIPTION:Title: The second universal motivic Chern class and cluster structure of modul
i spaces of G-local systems\nby Alexander Goncharov (Yale University)
as part of M-seminar\n\n\nAbstract\nThe second motivic Chern class is the
generator of the degree 4\, weight 2 motivic cohomology of BG\, where G is
a split simple algebraic group over Q. I will construct a collection of e
xplicit cocycles for the second motivic Chern class. It has a number of ap
plications\, such as local combinatorial formulas for the usual second Che
rn class of a G-bundle over a manifold\, or explicit constructions of the
determinant bundle on Bun(G)\, the extension of G by K_2 etc. The construc
tion is closely related to the cluster structure of the moduli space of de
corated G-local systems on a surface S with boundary.\n
LOCATION:https://researchseminars.org/talk/M-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20200910T203000Z
DTEND:20200910T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/22
DESCRIPTION:Title: Categorical g-actions for modules over truncated shifted Yangians\n
by Joel Kamnitzer (University of Toronto) as part of M-seminar\n\n\nAbstra
ct\nGiven a representation V of a reductive group G\, Braverman-Finkelberg
-Nakajima defined a Poisson variety called the Coulomb branch\, using a co
nvolution algebra construction. This variety comes with a natural deforma
tion quantization\, called a Coulomb branch algebra. Important cases of t
hese Coulomb branches are (generalized) affine Grassmannian slices\, and t
heir quantizations are truncated shifted Yangians.\nMotivated by the geome
tric Satake correspondence and the theory of symplectic duality/3d mirror
symmetry\, we expect a categorical g-action on modules for these truncated
shifted Yangians. I will explain three results in this direction. First
\, we have an indirect realization of this action\, using equivalences wit
h KLRW-modules. Second\, we have a geometric relation between these genera
lized slices by Hamiltonian reduction. Finally\, we have an algebraic ver
sion of this Hamiltonian reduction which we are able to relate to the firs
t realization.\n
LOCATION:https://researchseminars.org/talk/M-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Mellit (University of Vienna)
DTSTART:20200917T183000Z
DTEND:20200917T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/23
DESCRIPTION:Title: The curious hard Lefschetz property for character varieties\nby Ant
on Mellit (University of Vienna) as part of M-seminar\n\n\nAbstract\nI wil
l talk about a way to decompose various character varieties into cells whe
re each cell looks like a product of an affine space and a symplectic toru
s. This can be thought of as abelianization. As an application\, we deduce
the curious hard Lefschetz property conjectured by Hausel\, Letellier and
Rodriguez-Villegas\, which claims that the operator of cup product with t
he class of the holomorphic symplectic form is an isomorphism between comp
lementary degrees of the associated graded with respect to the weight filt
ration of the cohomology.\n
LOCATION:https://researchseminars.org/talk/M-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junxiao Wang (Northwestern University)
DTSTART:20200924T203000Z
DTEND:20200924T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/24
DESCRIPTION:Title: The Gamma Conjecture for the tropical 1-cycles in local mirror symmetry
\nby Junxiao Wang (Northwestern University) as part of M-seminar\n\n\n
Abstract\nThe Gamma Conjecture in mirror symmetry relates central charges
of dual objects. Mathematically\, periods of a Lagrangian submanifold are
related to characteristic classes of the mirror coherent sheaf. In this ta
lk\, I will test the Gamma Conjecture in the setting of local mirror symme
try. For a given coherent sheaf on the canonical bundle of a smooth toric
surface\, I will identify a 3-cycle in the mirror using tropical geometry
by comparing its period with the central charge of the coherent sheaf thro
ugh the Gamma Conjecture. If time permits\, I will also discuss about the
higher dimensional case. This work is based on Ruddat and Siebert's work o
n the period computation and is inspired by Abouzaid\, Ganatra\, Iritani a
nd Sheridan's work on the Gamma Conjecture.\n
LOCATION:https://researchseminars.org/talk/M-seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Okounkov (Columbia University)
DTSTART:20201001T203000Z
DTEND:20201001T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/25
DESCRIPTION:Title: Monodromy: yesterday\, today\, and tomorrow\nby Andrei Okounkov (Co
lumbia University) as part of M-seminar\n\n\nAbstract\nMonodromy of soluti
ons of differential equations is very much a recurring theme in mathematic
s\, from XIX century to the present day. For instance\, the Kohno-Drinfeld
theorem from 30+ years ago\, which describes the monodromy of the Knizhni
k-Zamolodchikov equations of the Conformal Field Theory in term of braidin
g for the associated quantum group\, as a striking example of how represen
tation-theoretic ideas may shed light on this problem. In this talk\, I wi
ll talk about some more recent advances that include ideas from enumerativ
e geometry and representation theory over a field of prime characteristic.
\n
LOCATION:https://researchseminars.org/talk/M-seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Cherkis (University of Arizona)
DTSTART:20201008T203000Z
DTEND:20201008T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/26
DESCRIPTION:Title: Doubly Periodic Monopoles and Exploded Geometry\nby Sergey Cherkis
(University of Arizona) as part of M-seminar\n\n\nAbstract\nClassical mono
pole dynamics captures both the geometry of the moduli spaces of quantum s
upersymmetric gauge theories and the dynamics of certain brane configurati
ons. It is also a good source of self-dual gravitational instantons -- hy
perkahler manifolds in real dimension four.\n\nAfter an overview of these
relations for various monopoles\, we shall focus on doubly periodic monopo
les and their moduli spaces. In particular\, the natural compactification
of these moduli spaces is formulated in terms of exploded geometry of Bre
tt Parker.\n
LOCATION:https://researchseminars.org/talk/M-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ron Donagi (University of Pennsylvania)
DTSTART:20201015T203000Z
DTEND:20201015T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/27
DESCRIPTION:Title: Families of Hitchin systems and N=2 theories\nby Ron Donagi (Univer
sity of Pennsylvania) as part of M-seminar\n\n\nAbstract\nMotivated by the
connection to 4d N=2 theories\, we study the global behavior of families
of tamely-ramified $SL_N$ Hitchin integrable systems as the underlying cur
ve varies over the Deligne-Mumford moduli space of stable pointed curves.
In particular\, we describe a flat degeneration of the Hitchin system to a
nodal base curve and show that the behaviour of the integrable system at
the node is partially encoded in a pair (O\,H) where O is a nilpotent orbi
t and H is a simple Lie subgroup of FO\, the flavour symmetry group associ
ated to O. The family of Hitchin systems is nontrivially-fibered over the
Deligne-Mumford moduli space. We prove a non-obvious result that the Hitch
in bases fit together to form a vector bundle over the compactified moduli
space. For the particular case of $M_{0\,4}$\, we compute this vector bun
dle explicitly. Finally\, we give a classification of the allowed pairs (O
\,H) that can arise for any given N. (This is joint work with Aswin Balasu
bramanian and Jacques Distler)\n
LOCATION:https://researchseminars.org/talk/M-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zack Sylvan (Columbia University)
DTSTART:20201022T203000Z
DTEND:20201022T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/28
DESCRIPTION:Title: Homological mirror symmetry near SYZ singularities\nby Zack Sylvan
(Columbia University) as part of M-seminar\n\n\nAbstract\nI'll discuss hom
ological mirror symmetry for the spaces $\\prod x_i=1+\\sum y_j$\, which a
ppear as neighborhoods of SYZ singularities. I'll start by discussing wrap
ped HMS\, and then I'll explain how to cook up a torus-like closed Lagrang
ian brane for every point of the mirror. This is work in progress with M.
Abouzaid and in part with A. Perry.\n
LOCATION:https://researchseminars.org/talk/M-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Yue Yu (Université Paris-Sud)
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/29
DESCRIPTION:Title: Frobenius structure conjecture and application to cluster algebras\
nby Tony Yue Yu (Université Paris-Sud) as part of M-seminar\n\n\nAbstract
\nI will explain the Frobenius structure conjecture of Gross-Hacking-Keel
in mirror symmetry\, and an application towards cluster algebras. I will s
how that the naive counts of rational curves in an affine log Calabi-Yau v
ariety U\, containing an open algebraic torus\, determine in a simple way\
, a mirror family of log Calabi-Yau varieties\, as the spectrum of a commu
tative associative algebra equipped with a multilinear form. The structure
constants of the algebra are constructed via counting non-archimedean ana
lytic disks in the analytification of U. I will explain various properties
of the counting\, notably deformation invariance\, symmetry\, gluing form
ula and convexity. In the special case when U is a Fock-Goncharov skew-sym
metric X-cluster variety\, our algebra generalizes\, and in particular giv
es a direct geometric construction of\, the mirror algebra of Gross-Hackin
g-Keel-Kontsevich. The comparison is proved via a canonical scattering dia
gram defined by counting infinitesimal non-archimedean analytic cylinders\
, without using the Kontsevich-Soibelman algorithm. Several combinatorial
conjectures of GHKK follow readily from the geometric description. This is
joint work with S. Keel\, arXiv:1908.09861. If time permits\, I will ment
ion another application towards the moduli space of KSBA stable pairs\, jo
int with P. Hacking and S. Keel\, arXiv: 2008.02299.\n
LOCATION:https://researchseminars.org/talk/M-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Harvard University)
DTSTART:20201105T213000Z
DTEND:20201105T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/30
DESCRIPTION:Title: The moduli space of l-adic local systems and application to geometric a
nd classical Langlands theory\nby Dennis Gaitsgory (Harvard University
) as part of M-seminar\n\n\nAbstract\nIn the talk we will define a new geo
metric object\, the stack of local systems with restricted variation. We w
ill discuss the appropriately modified version of the geometric Langlands
conjecture and its relationship with the classical Langlands conjecture vi
a the operation of categorical trace of Frobenius.\n
LOCATION:https://researchseminars.org/talk/M-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoosik Kim (Brandeis University)
DTSTART:20201112T213000Z
DTEND:20201112T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/31
DESCRIPTION:Title: Disc potential functions of Quadrics\nby Yoosik Kim (Brandeis Unive
rsity) as part of M-seminar\n\n\nAbstract\nA disc potential function intro
duced by Fukaya—Oh—Ohta—Ono plays an important role in studying Lagr
angian submanifolds and the ambient symplectic manifold. In this talk\, I
will explain how to compute the disc potential function of quadrics. The p
otential function provides the Landau-Ginzburg mirror\, which agrees with
Przyjalkowski’s mirror and a cluster chart of Pech—Rietsch—Williams
’ mirror.\n
LOCATION:https://researchseminars.org/talk/M-seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Shende (UC Berkeley)
DTSTART:20201119T193000Z
DTEND:20201119T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/32
DESCRIPTION:Title: Sheaf quantization in Weinstein symplectic manifolds\nby Vivek Shen
de (UC Berkeley) as part of M-seminar\n\n\nAbstract\nI will explain how\,
using only the microlocal sheaf theory (i.e. no holomorphic curves)\, one
can produce a category associated to a Weinstein symplectic manifold. Exa
ct Lagrangians will give objects of this category. This is work with Davi
d Nadler. (A posteriori\, it is possible to show that this category is eq
uivalent to the Fukaya category\, but that is a long and different story).
\n
LOCATION:https://researchseminars.org/talk/M-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nekrasov (Simons Center for Geometry and Physics)
DTSTART:20201203T213000Z
DTEND:20201203T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/33
DESCRIPTION:Title: Towards Lefschetz thimbles in field theory\nby Nikita Nekrasov (Sim
ons Center for Geometry and Physics) as part of M-seminar\n\n\nAbstract\nI
will review the quantization procedure viewed from a higher dimensional p
erspective: old-fashioned path integrals\, Kontsevich Poisson sigma model\
, cc branes of Kapustin-Orlov\, and\, finally\, four dimensional Omega-de
formed N=2 gauge theories. By rephrasing the computation of quantum model
partition function in four dimensional language we arrive at the motivatio
n to search for critical points of analytically continued (complexified) a
ction functional. I will then report on the recent progress (in a joint wo
rk with I.Krichever) in this problem in the case of two dimensional sigma
models\, notably with the target spaces being the spheres and complex proj
ective spaces.\n
LOCATION:https://researchseminars.org/talk/M-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Addington (University of Oregon)
DTSTART:20210128T213000Z
DTEND:20210128T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/34
DESCRIPTION:Title: Derived autoequivalences of moduli spaces of sheaves on K3 surfaces
\nby Nicolas Addington (University of Oregon) as part of M-seminar\n\n\nAb
stract\nSome years ago I constructed a new autoequivalence of the derived
category\nof the Hilbert scheme of n points on a K3 surface using "P-funct
ors."\nLater Donovan\, Meachan\, and I extended the construction to some m
oduli\nspaces of torsion sheaves\, and illuminated the geometric meaning o
f the\nstory. Now my student Andrew Wray and I can extend it to moduli sp
aces of\nsheaves of any rank\, powered by a new proof of the standard resu
lts about\nthose moduli spaces. We deform to a Hilbert scheme in one step
\, using\ntwistor lines.\n
LOCATION:https://researchseminars.org/talk/M-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Gaiotto (Perimeter Institute for Theoretical Physics)
DTSTART:20210204T213000Z
DTEND:20210204T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/35
DESCRIPTION:Title: Brane quantization\nby Davide Gaiotto (Perimeter Institute for Theo
retical Physics) as part of M-seminar\n\n\nAbstract\nI will review the A-m
odel Gukov-Witten setup for the quantization of a phase space and its rela
tion to the analytic version of the Langlands correspondence recently prop
osed by Etingof\, Frenkel and Kazhdan.\n
LOCATION:https://researchseminars.org/talk/M-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Joyce (University of Oxford)
DTSTART:20210211T170000Z
DTEND:20210211T180000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/36
DESCRIPTION:Title: Enumerative invariants in Algebraic Geometry and wall crossing formulae
\nby Dominic Joyce (University of Oxford) as part of M-seminar\n\n\nAb
stract\nIn Gross-Joyce-Tanaka arXiv:2005.05637\, we described a universal
conjectural picture for enumerative invariants counting semistable objects
in abelian categories/gauge theories\, which claimed that under some assu
mptions:\n (i) one can construct invariants\, as virtual classes in the ra
tional homology of the “projective linear” moduli stack\, for all topo
logical invariants (fixed Chern classes etc)\, including classes with stri
ctly semistables\;\n (ii) these invariants satisfy a wall-crossing formula
under change of stability condition\, written in terms of a Lie bracket o
n the homology of the moduli stack\, which came out of my project on verte
x algebra structures on homology of moduli stacks.\nWe proved the conjectu
re for representations of acyclic quivers.\n In work in progress\, I hav
e now proved/am proving versions of the conjectures for a broad family of
settings in Algebraic Geometry\, in which invariants are formed using Behr
end-Fantechi virtual classes. These include suitable quivers with relation
s\, coherent sheaves on curves\, surfaces and some 3-folds\, and algebraic
Seiberg-Witten invariants and Donaldson invariants of projective complex
surfaces. The SW/Donaldson theory picture includes wall-crossing formulae\
, related to those of Mochizuki\, which implicitly determine algebraic U(n
) and SU(n) Donaldson invariants\, of any rank\, in terms of rank 1 Seiber
g-Witten type invariants and invariants of Hilbert schemes of points\, for
any projective complex surface\, without restriction on $b^1$\, or $b^2_+
$\, or a simple type assumption.\n The talk will give an overview of this
programme.\n
LOCATION:https://researchseminars.org/talk/M-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Efimov (Steklov Institute for Mathematics)
DTSTART:20210218T170000Z
DTEND:20210218T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/37
DESCRIPTION:Title: Nuclear modules over proper DG algebras\nby Alexander Efimov (Stekl
ov Institute for Mathematics) as part of M-seminar\n\n\nAbstract\nI will e
xplain a certain general natural construction of a dualizable presentable
DG category Nuc(A) associated with a proper DG algebra (or a proper DG cat
egory) A over a commutative ring k. As a special case\, it gives (an "unbo
unded" version of) the category of nuclear modules on a formal scheme\, wh
ich was defined recently by Clausen and Scholze.\n The compact objects of
Nuc(A) are given by (the usual) pseudo-perfect A-modules PsPerf(A) (i.e.
those A-modules which are perfect over k). However\, unlike PsPerf(A)\, th
e category Nuc(A) has very nice properties: it satisfies Zariski descent o
ver Spec(k)\, and so does its continuous K-theory. Moreover\, its continuo
us K-theory and Hochschild homology are expected to have a very concrete d
escription in terms of A.\n I will also explain that Nuc(A) is a special
case of an even more general notion/construction\, which (surprisingly) wa
s not considered before: internal Hom in the symmetric monoidal category\,
whose objects are dualizable presentable DG categories\, and the morphism
s are given by strongly continuous functors (i.e. the functors whose right
adjoint commutes with infinite direct sums).\n
LOCATION:https://researchseminars.org/talk/M-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Nadler (UC Berkeley)
DTSTART:20210225T213000Z
DTEND:20210225T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/38
DESCRIPTION:Title: Verlinde formulas in Betti Geometric Langlands\nby David Nadler (UC
Berkeley) as part of M-seminar\n\n\nAbstract\nI'll review the Betti varia
nt of Geometric Langlands then describe progress towards expressing automo
rphic categories of smooth curves in terms of such categories for marked g
enus zero curves. Time permitting I'll discuss specific applications in lo
w genus. Joint work with Zhiwei Yun.\n
LOCATION:https://researchseminars.org/talk/M-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Weekes (University of British Columbia)
DTSTART:20210304T213000Z
DTEND:20210304T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/39
DESCRIPTION:Title: Coulomb branches for quiver gauge theories with symmetrizers\nby Al
ex Weekes (University of British Columbia) as part of M-seminar\n\n\nAbstr
act\nBraverman-Finkelberg-Nakajima have recently given a mathematical cons
truction of the Coulomb branches for 3d N=4 theories. From a representatio
n-theoretic perspective\, one reason that their work is especially appeali
ng is that affine Grassmannian slices of ADE types arise this way\, associ
ated to quiver gauge theories. By allowing general quivers\, Coulomb branc
hes also provide a candidate definition for affine Grassmannian slices in
all symmetric Kac-Moody types. In this talk I will discuss joint work with
Nakajima\, where we generalize the BFN construction of the Coulomb branch
to incorporate "symmetrizers". In this way we recover affine Grassmannian
slices in BCFG type\, and a candidate definition for symmetrizable Kac-Mo
ody types.\n
LOCATION:https://researchseminars.org/talk/M-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Caldararu (University of Wisconsin-Madison)
DTSTART:20210311T213000Z
DTEND:20210311T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/40
DESCRIPTION:Title: A survey of categorical enumerative invariants\nby Andrei Caldararu
(University of Wisconsin-Madison) as part of M-seminar\n\n\nAbstract\nI w
ill survey recent progress in defining and computing categorical enumerati
ve invariants\, analogues of Gromov-Witten invariants defined directly fro
m a cyclic $A_\\infty$-category and a choice of splitting of the Hodge fil
tration on its periodic cyclic homology. A proposed definition of such inv
ariants appeared in 2005 in work of Costello\, but the original approach h
ad technical problems that made computations impossible. New results allow
us to give an alternate definition of Costello's invariants\, where expli
cit computation is possible -- and indeed we apply our results to B-model
calculations for elliptic curves and categories of matrix factorizations.
My talk is based on joint work with Junwu Tu and Kevin Costello.\n
LOCATION:https://researchseminars.org/talk/M-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Soibelman (IHES)
DTSTART:20210318T183000Z
DTEND:20210318T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/41
DESCRIPTION:Title: Motivic invariants for moduli of parabolic Higgs bundles and parabolic
connections on a curve\nby Alexander Soibelman (IHES) as part of M-sem
inar\n\n\nAbstract\nMotivic classes can realize certain algebro-geometric
invariants using elements of the Grothendieck ring of varieties or\, more
generally\, of stacks. I will introduce motivic classes through rational p
oint counting over a finite field\, then discuss motivic class computation
s for moduli spaces and moduli stacks of semistable Higgs bundles (as well
as vector bundles with connections on a curve)\, and finish by addressing
the parabolic case.\n
LOCATION:https://researchseminars.org/talk/M-seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Polishchuk (University of Oregon)
DTSTART:20210325T203000Z
DTEND:20210325T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/42
DESCRIPTION:Title: Supermeasure on moduli of supercurves\nby Alexander Polishchuk (Uni
versity of Oregon) as part of M-seminar\n\n\nAbstract\nThis is a report on
joint work with Giovanni Felder and David Kazhdan. I will discuss the mod
uli space of supercurves and its compactification\, the moduli of stable s
upercurves. As in the classical case\, the analog of Mumford’s isomorphi
sm gives an expression of the canonical bundle on this moduli space in ter
ms of the Berezinian of the Hodge bundle. We consider the corresponding su
permeasure obtained from this isomorphism together with the natural hermit
ian metric on the Hodge bundle. Our main results concern its polar behavio
ur at infinity and on the null-theta divisor.\n
LOCATION:https://researchseminars.org/talk/M-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Rimanyi (University of North Carolina)
DTSTART:20210401T203000Z
DTEND:20210401T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/43
DESCRIPTION:Title: 3d mirror symmetry for characteristic classes of bow varieties\nby
Richard Rimanyi (University of North Carolina) as part of M-seminar\n\n\nA
bstract\nOne of the predictions of N=4 d=3 mirror symmetry concerns charac
teristic classes\, namely so-called stable envelopes of singularities. We
will explore the notion of stable envelopes\, their role in enumerative ge
ometry and representation theory. Then we will discuss Cherkis bow varieti
es that come in pairs (3d mirror pairs) such that the elliptic stable enve
lopes on two spaces in a pair conjecturally "coincide" (after transpositi
on\, switching equivariant and dynamical variables\, and inverting ℏ).\n
LOCATION:https://researchseminars.org/talk/M-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Webster (Perimeter Institute for Theoretical Physics)
DTSTART:20210408T203000Z
DTEND:20210408T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/44
DESCRIPTION:Title: Knot homology and coherent sheaves on Coulomb branches\nby Ben Webs
ter (Perimeter Institute for Theoretical Physics) as part of M-seminar\n\n
\nAbstract\nRecent work of Aganagic proposes the construction of a homolog
ical knot invariant categorifying the Reshetikhin-Turaev invariants of min
iscule representations of type ADE Lie algebras\, using the geometry and p
hysics of coherent sheaves on a space which one can alternately describe a
s a resolved slice in the affine Grassmannian\, a space of G-monopoles wit
h specified singularities\, or as the Coulomb branch of the corresponding
3d quiver gauge theories. We give a mathematically rigorous construction o
f this invariant\, and in fact extend it to an invariant of annular knots\
, using the theory of line operators in the quiver gauge theory and their
relationship to non-commutative resolutions of these varieties (generalizi
ng Bezrukavnikov's non-commutative Springer resolution).\n
LOCATION:https://researchseminars.org/talk/M-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammed Abouzaid (Columbia University)
DTSTART:20210415T193000Z
DTEND:20210415T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/45
DESCRIPTION:Title: Arnol'd Conjecture and Morava K-theory\nby Mohammed Abouzaid (Colum
bia University) as part of M-seminar\n\n\nAbstract\nThe Arnol'd conjecture
on the minimal number of fixed points of a Hamiltonian diffeomorphism has
motivated a large number of developments in symplectic topology over the
last few decades. I will explain a proof\, joint with Blumberg\, that the
number of such fixed points is larger than the rank of the homology with c
oefficients in any field. The proof will involve developing tools and meth
ods of Floer homotopy theory.\n
LOCATION:https://researchseminars.org/talk/M-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Seidel (MIT)
DTSTART:20210422T203000Z
DTEND:20210422T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/46
DESCRIPTION:Title: Fukaya categories of Calabi-Yau hypersurfaces\nby Paul Seidel (MIT)
as part of M-seminar\n\n\nAbstract\nWe will discuss some structural prope
rties of the Fukaya categories of Calabi-Yau hypersurfaces\, concerning th
eir dependence on the Kaehler (Novikov) parameter\, that can be proved wit
hout relying on homological mirror symmetry.\n
LOCATION:https://researchseminars.org/talk/M-seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Simpson (University of Nice)
DTSTART:20210429T203000Z
DTEND:20210429T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/47
DESCRIPTION:Title: On some Fukaya categories of singular Lagrangians with coefficients
\nby Carlos Simpson (University of Nice) as part of M-seminar\n\n\nAbstrac
t\nThis is about work in progress with Fabian Haiden and Ludmil Katzarkov.
We consider the folkloric construction of Fukaya categories over the Nov
ikov ring\, for objects that are graphs in a surface (the complex plane) t
ogether with sections of a fiber dg-category patched together with A_n-obj
ects at (n+1)-fold vertices of the graph. We discuss aspects of the questi
on of defining these categories\, and then look at the case of 6 endpoints
on a regular hexagon with A_2 coefficient category. Mirror symmetry alrea
dy gives a stability condition\, and we show that the semistable objects a
re represented by spectral networks that can be pictured in an explicit wa
y.\n
LOCATION:https://researchseminars.org/talk/M-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Mirković (University of Massachusetts (Amherst))
DTSTART:20210506T203000Z
DTEND:20210506T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/48
DESCRIPTION:Title: Loop Grassmannians of lattices\nby Ivan Mirković (University of Ma
ssachusetts (Amherst)) as part of M-seminar\n\n\nAbstract\nTo each choice
of a based lattice L\, a cohomology theory A and a poset\nP one can associ
ate a space Gr(L\,A\,P). This generalizes the loop Grassmannians of\nsemis
imple groups which is the case of the coroot lattice\, classical cohomolog
y and\nthe point poset.\nThis is an attempt to replace reductive groups (i
n some aspects) by “coliding particles”.\nOne could also view it as an
approach to loop Grassmannians through homology rather\nthan cohomology\,
motivated by the Contou-Carrere symbol.\n
LOCATION:https://researchseminars.org/talk/M-seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Auroux (Harvard University)
DTSTART:20210916T210000Z
DTEND:20210916T220000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/49
DESCRIPTION:Title: Lagrangian Floer theory for trivalent graphs and HMS for curves\nby
Denis Auroux (Harvard University) as part of M-seminar\n\n\nAbstract\nThe
mirror of a genus g curve can be viewed as a trivalent\nconfiguration of
3g−3 rational curves meeting in 2g−2 triple points\;\nmore precisely\,
this singular configuration arises as the critical locus\nof the superpot
ential in a 3-dimensional Landau-Ginzburg mirror. In\njoint work with Alex
ander Efimov and Ludmil Katzarkov\, we introduce a\nnotion of Fukaya categ
ory for such a configuration of rational curves\,\nwhere objects are embed
ded graphs with trivalent vertices at the triple\npoints\, and morphisms a
re linear combinations of intersection points as\nin usual Floer theory. W
e will describe the construction of the\nstructure maps of these Fukaya ca
tegories\, attempt to provide some\nmotivation\, and outline examples of c
alculations that can be carried out\nto verify homological mirror symmetry
in this setting.\n
LOCATION:https://researchseminars.org/talk/M-seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Moore (Rutgers University)
DTSTART:20210922T203000Z
DTEND:20210922T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/50
DESCRIPTION:Title: 2d Categorical Wall-Crossing With Twisted Masses\nby Greg Moore (Ru
tgers University) as part of M-seminar\n\n\nAbstract\nWe review how supers
ymmetric quantum mechanics naturally leads to several standard constructio
ns in homological algebra. We apply these ideas to 2d Landau-Ginzburg mode
ls with (2\,2) supersymmetry to discuss wall-crossing. Some aspects of the
web formalism are reviewed and applied to the categorification of the Cec
otti-Vafa wall-crossing formula for BPS invariants. We then sketch the gen
eralization to include twisted masses. In the final part of the talk we sk
etch how some of these ideas give a natural framework for understanding a
recent conjecture of Garoufalidis\, Gu\, and Marino and lead to potentiall
y new knot invariants. The talk is based on work done with Ahsan Khan and
the final part is the result of discussions with Ahsan Khan\, Davide Gaiot
to\, and Fei Yan.\n
LOCATION:https://researchseminars.org/talk/M-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Braverman (University of Toronto and Perimeter Institute
)
DTSTART:20210930T203000Z
DTEND:20210930T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/51
DESCRIPTION:Title: Universal Coulomb branch and theta-sheaves\nby Alexander Braverman
(University of Toronto and Perimeter Institute) as part of M-seminar\n\n\n
Abstract\nIn the first half of the talk I shall recall basic definitions r
elated to derived geometric Satake equivalence and its relation to constru
ction of Coulomb branches of 3d N=4 gauge theories (no physics background
is assumed). In the 2nd half I will describe certain "universal Coulomb ob
ject" on the affine Grassmannian of the group Sp(2n) (following suggestion
s by Drinfeld and Raskin) and discuss its relation with the so called thet
a-sheaf studied by Lafforgue and Lysenko.\n
LOCATION:https://researchseminars.org/talk/M-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamas Hausel (IST Austria)
DTSTART:20211007T180000Z
DTEND:20211007T190000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/52
DESCRIPTION:Title: Explicit Hitchin System on Lagrangians\nby Tamas Hausel (IST Austri
a) as part of M-seminar\n\n\nAbstract\nI will report on joint project with
Hitchin where we compute some examples of the multiplicity algebra of the
Hitchin system on upward flows as jet schemes of cohomology rings of Gras
smannians.\n
LOCATION:https://researchseminars.org/talk/M-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Shende (University of Southern Denmark)
DTSTART:20211014T183000Z
DTEND:20211014T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/53
DESCRIPTION:Title: Localization of Fukaya categories and quantizing the Hitchin system
\nby Vivek Shende (University of Southern Denmark) as part of M-seminar\n\
n\nAbstract\nFor a complex curve C and reductive group G\, the space of G-
bundles on C has been of much interest to many mathematicians. For the pu
rposes of the geometric Langlands correspondence\, one wishes to construct
certain `Hecke eigensheaves' over this space. It has long been expected
(and in some cases known) that these should arise from quantization of fib
ers of Hitchin's integrable system\, this being the map h: T*Bun(C\, G) --
> A which\, for G = GL(n)\, records the spectral curve of a Higgs bundle.
Historically this means that one tries to associate a D-module on Bun(C\,
G) to each fiber of h.\n\nMore recently\, the fact that Langlands dual gr
oups give rise to dual Hitchin fibrations has led to the expectation that
geometric Langlands duality should be some sort of homological mirror symm
etry. In this talk we will take a step towards making this precise: recen
t results on the localization of wrapped Fukaya categories allow us to use
Floer theory to associate a constructible sheaf on Bun(C\, G) to a fiber
of the Hitchin fibration. (More precisely\, we may do for smooth fibers\,
in components of Bun(C\, G) where there are no strictly semistable Higgs
bundles\, and should assume G connected center). We don't yet know how to
check that we have eigensheaves\, but can check some expected properties:
our sheaves have the expected endomorphisms\, rank\, microstalks on certa
in components\, and sheaves from different fibers are orthogonal.\n
LOCATION:https://researchseminars.org/talk/M-seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Odesskii (Brock University)
DTSTART:20211021T180000Z
DTEND:20211021T190000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/54
DESCRIPTION:Title: Multiplication kernels\nby Alexander Odesskii (Brock University) as
part of M-seminar\n\n\nAbstract\nCommutative associative multiplications
on a space of functions can be defined in terms of multiplication kernels
which are an infinite-dimensional analog of structure constants of multipl
ication in finite-dimensional case. Associativity constrain gives an integ
ral equation for multiplication kernel. I will explain various ways of dea
ling with this integral equation in purely algebraic terms. In particular\
, connections with integrable systems will be discussed and a lot of examp
les will be constructed. The talk is based on the paper M. Kontsevich\, A.
Odesski Multiplication kernels\, arXiv:2105.04238\n
LOCATION:https://researchseminars.org/talk/M-seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20211025T183000Z
DTEND:20211025T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/55
DESCRIPTION:Title: Cohomological DT theory and nonabelian Hodge theory for stacks - 1\
nby Ben Davison (University of Edinburgh) as part of M-seminar\n\n\nAbstra
ct\n(this talk is a part of a three-lectures minicourse)\n\nThe nonabelian
Hodge correspondence provides a diffeomorphism between certain coarse mod
uli spaces of semistable Higgs bundles on a smooth projective curve C (the
Dolbeault side) and coarse moduli spaces of representations of the fundam
ental group of C (the Betti side). In the case of coprime rank and degree
\, these spaces are smooth\, and the famous P=W conjecture states that the
isomorphism in cohomology provided by the above diffeomorphism takes the
weight filtration on the Betti side to the perverse filtration on the Dolb
eault side. The purpose of these talks is to use recent advances in cohom
ological Donaldson-Thomas theory to extend this story to moduli stacks.\nF
or coprime rank and degree\, two key features in the study of classical no
nabelian Hodge theory are the perverse filtration with respect to the Hitc
hin base\, and the purity of the cohomology of the Dolbeault moduli space.
I will present an extension of the BBDG decomposition theorem to moduli
stacks of objects in 2CY categories\, which enables us to reproduce both o
f the above features for stacks in nonabelian Hodge theory.\nThese results
\, along with cohomological Hall algebras\, allow us to connect the inters
ection cohomology of coarse moduli spaces with the Borel-Moore homology of
the above stacks\, providing the connection between three versions of the
P=W conjecture: the original conjecture for smooth moduli spaces\, the ve
rsion for intersection cohomology of singular moduli spaces\, and a new ve
rsion for stacks.\n
LOCATION:https://researchseminars.org/talk/M-seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20211027T183000Z
DTEND:20211027T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/56
DESCRIPTION:Title: Cohomological DT theory and nonabelian Hodge theory for stacks - 2\
nby Ben Davison (University of Edinburgh) as part of M-seminar\n\n\nAbstra
ct\n(this talk is a part of a three-lectures minicourse)\n\nThe nonabelian
Hodge correspondence provides a diffeomorphism between certain coarse mod
uli spaces of semistable Higgs bundles on a smooth projective curve C (the
Dolbeault side) and coarse moduli spaces of representations of the fundam
ental group of C (the Betti side). In the case of coprime rank and degree
\, these spaces are smooth\, and the famous P=W conjecture states that the
isomorphism in cohomology provided by the above diffeomorphism takes the
weight filtration on the Betti side to the perverse filtration on the Dolb
eault side. The purpose of these talks is to use recent advances in cohom
ological Donaldson-Thomas theory to extend this story to moduli stacks.\nF
or coprime rank and degree\, two key features in the study of classical no
nabelian Hodge theory are the perverse filtration with respect to the Hitc
hin base\, and the purity of the cohomology of the Dolbeault moduli space.
I will present an extension of the BBDG decomposition theorem to moduli
stacks of objects in 2CY categories\, which enables us to reproduce both o
f the above features for stacks in nonabelian Hodge theory.\nThese results
\, along with cohomological Hall algebras\, allow us to connect the inters
ection cohomology of coarse moduli spaces with the Borel-Moore homology of
the above stacks\, providing the connection between three versions of the
P=W conjecture: the original conjecture for smooth moduli spaces\, the ve
rsion for intersection cohomology of singular moduli spaces\, and a new ve
rsion for stacks.\n
LOCATION:https://researchseminars.org/talk/M-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20211028T183000Z
DTEND:20211028T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/57
DESCRIPTION:Title: Cohomological DT theory and nonabelian Hodge theory for stacks - 3\
nby Ben Davison (University of Edinburgh) as part of M-seminar\n\n\nAbstra
ct\n(this talk is a part of a three-lectures minicourse)\n\nThe nonabelian
Hodge correspondence provides a diffeomorphism between certain coarse mod
uli spaces of semistable Higgs bundles on a smooth projective curve C (the
Dolbeault side) and coarse moduli spaces of representations of the fundam
ental group of C (the Betti side). In the case of coprime rank and degree
\, these spaces are smooth\, and the famous P=W conjecture states that the
isomorphism in cohomology provided by the above diffeomorphism takes the
weight filtration on the Betti side to the perverse filtration on the Dolb
eault side. The purpose of these talks is to use recent advances in cohom
ological Donaldson-Thomas theory to extend this story to moduli stacks.\nF
or coprime rank and degree\, two key features in the study of classical no
nabelian Hodge theory are the perverse filtration with respect to the Hitc
hin base\, and the purity of the cohomology of the Dolbeault moduli space.
I will present an extension of the BBDG decomposition theorem to moduli
stacks of objects in 2CY categories\, which enables us to reproduce both o
f the above features for stacks in nonabelian Hodge theory.\nThese results
\, along with cohomological Hall algebras\, allow us to connect the inters
ection cohomology of coarse moduli spaces with the Borel-Moore homology of
the above stacks\, providing the connection between three versions of the
P=W conjecture: the original conjecture for smooth moduli spaces\, the ve
rsion for intersection cohomology of singular moduli spaces\, and a new ve
rsion for stacks.\n
LOCATION:https://researchseminars.org/talk/M-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHES)
DTSTART:20211104T160000Z
DTEND:20211104T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/58
DESCRIPTION:Title: On the perturbation theory for spectra in quantum mechanics\nby Max
im Kontsevich (IHES) as part of M-seminar\n\n\nAbstract\nConsider a polyno
mial differential operator in one variable\, depending on a small paramete
r (Planck constant). Under appropriate conditions\, the low-energy spectru
m admits an asymptotic expansion in hbar. I will present a way to calculat
e such series via a purely "commutative problem"\, a mixture of variations
of Hodge structures and of the Stirling formula. This result came from di
scussions with A. Soibelman.\n
LOCATION:https://researchseminars.org/talk/M-seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Goncharov (Yale University)
DTSTART:20211111T213000Z
DTEND:20211111T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/59
DESCRIPTION:Title: Spectral description of non-commutative local systems on surfaces\n
by Alexander Goncharov (Yale University) as part of M-seminar\n\n\nAbstrac
t\nLet R be a non-commutative field. I plan to give a cluster description
of the following moduli spaces:\n\ni) Triples of flags in generic positio
n.\n\nii) Moduli spaces R-vector bundles with flat framed connections over
topological surfaces with corners.\n\niii) Moduli spaces of non-commutati
ve Stokes data.\n\nEach of the last two examples includes the previous one
as a special case. This is a joint work with Maxim Kontsevich.\n
LOCATION:https://researchseminars.org/talk/M-seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Columbia University)
DTSTART:20211118T213000Z
DTEND:20211118T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/60
DESCRIPTION:Title: Relative stable pairs and a non-Calabi-Yau wall crossing\nby Tudor
Padurariu (Columbia University) as part of M-seminar\n\n\nAbstract\nFor co
mplex smooth threefolds\, there are enumerative theories of curves defined
using sheaves\, such as Donaldson-Thomas (DT) theory using ideal sheaves
and Pandharipande-Thomas (PT) theory using stable pairs. These theories ar
e conjecturally related among themselves and conjecturally related to othe
r enumerative theories of curves\, such as Gromov-Witten theory. The conj
ectural relation between DT and PT theories is known only for Calabi-Yau t
hreefolds by work of Bridgeland\, Toda\, where one can use the powerful ma
chinery of motivic Hall algebras due to Joyce and his collaborators.\n\nBr
yan-Steinberg (BS) defined enumerative invariants for Calabi-Yau threefold
s Y with certain contraction maps Y→X. I plan to explain how to extend t
heir definition beyond the Calabi-Yau case and what is the conjectural rel
ation to the other enumerative theories. This conjectural relation is know
n in the Calabi-Yau case by work of Bryan-Steinberg using the motivic Hall
algebra. In contrast to the DT/ PT correspondence\, we manage to establis
h the BS/ PT correspondence in some non-Calabi-Yau situations.\n
LOCATION:https://researchseminars.org/talk/M-seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miroslav Rapcak (UC Berkeley)
DTSTART:20211202T213000Z
DTEND:20211202T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/61
DESCRIPTION:Title: $W_\\infty$ modules and melted crystals of DT and PT\nby Miroslav R
apcak (UC Berkeley) as part of M-seminar\n\n\nAbstract\n$W_\\infty$ algebr
a is a vertex operator algebra extending the Virasoro algebra by fields of
spin $3\,4\,\\dots$. It is known to admit a nice class of modules labelle
d by a triple of partitions. $W_\\infty$ is also known to admit an alterna
tive description in terms of the affine Yangian of $gl_1$ admitting a very
concrete definition of such modules. As we will see in this talk\, utiliz
ing the charge-conjugation automorphism of $W_\\infty$ in the language of
the affine Yangian leads to a new class of affine Yangian modules with non
-diagonalizable action of Cartan generators and striking connection with P
andharipande-Thomas invariants.\n
LOCATION:https://researchseminars.org/talk/M-seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenji Fukaya (Simons Center for Geometry and Physics)
DTSTART:20211209T213000Z
DTEND:20211209T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/62
DESCRIPTION:Title: A note on homological mirror symmetry over Novikov ring\nby Kenji F
ukaya (Simons Center for Geometry and Physics) as part of M-seminar\n\n\nA
bstract\nHomological Mirror symmetry is a symmetry between symplectic and
complex geometries. In the symplectic side\, Lagrangian Floer homology is
the main object of the study. In most of the results on homological mirror
symmetry in the literature\, Lagrangian Floer homology is considered over
the coefficient ring which is either a ground ring (such as Z\, Q\, C) or
a Novikov field\, where the formal parameter is inverted. Lagrangian Flo
er homology over Novikov ring is known to contain much more informations t
han one over Novikov field. In this talk\, I will explain certain ideas an
d preliminary results to study homological Mirror symmetry over Novikov r
ing. I will explain how the notion of Gromov-Hausdorff convergence of A in
finity category is used for this purpose.\n
LOCATION:https://researchseminars.org/talk/M-seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ginzburg (University of Chicago)
DTSTART:20220121T220000Z
DTEND:20220121T230000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/63
DESCRIPTION:Title: Chern classes of quantizable sheaves and characteristic cycles\nby
Victor Ginzburg (University of Chicago) as part of M-seminar\n\n\nAbstract
\nLet A be a formal deformation quantization of the structure sheaf of an
algebraic symplectic manifold X. Given a coherent sheaf E on X we define
a characteristic class s(E) as a product of the Chern character of E and a
certain class associated with the quantization A. We show that if E can b
e quantized to an A-module then all homogeneous components of s(E) in a ce
rtain range of degrees vanish. The proof is based on relating the Chern ch
aracters of E and of its quantization. The latter lives in the negative cy
clic homology of A and we show that the negative cyclic homology groups of
relevant degrees vanish.\n\nIn the holonomic case our result says that if
the support of the quantizable sheaf E is a (possibly singular) Lagrangi
an subvariety\, then the only nonvanishing Chern class of E is the top deg
ree class which is the Poincare dual of support cycle of E. As an applicat
ion\, let X be a conical symplectic resolution and B the algebra of global
sections of a filtered quantization of X. We prove\, motivated by a ques
tion by Bezrukavnikov and Losev\, that the characteristic cycles of finite
dimensional simple B-modules are linearly independent.\n
LOCATION:https://researchseminars.org/talk/M-seminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Rozansky (University of North Carolina)
DTSTART:20220127T213000Z
DTEND:20220127T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/64
DESCRIPTION:Title: Link homology from a stack of D2 branes with a B-twist\nby Lev Roza
nsky (University of North Carolina) as part of M-seminar\n\n\nAbstract\nTh
is is a joint work with A. Oblomkov. The HOMFLY-PT polynomial invariant of
a link in S^3 is `a sibling' of the DT invariant of a Calabi-Yau 3-fold X
: the difference is that the HOMFLY-PT polynomial counts the curves in X i
n the presence of special Lagrangian submanifolds related to link componen
ts. We construct a categorification of the HOMFLY-PT polynomial based on a
particular way of curve counting\, when the curves are almost coincident
and one has to account for their joint vibrations in a transverse C^2. Thu
s we select a special object FL in a 2-category associated with the Hilber
t scheme of n points in C^2\, define a homomorphism from the n-strand brai
d group to the monoidal category End(FL) and use it to associate a graded
vector space (homology) to the closure of a braid. I will explain the deta
ils of the mathematical construction and its interpretation within the M-t
heory.\n
LOCATION:https://researchseminars.org/talk/M-seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Mozgovoy (Trinity College (Dublin))
DTSTART:20220203T180000Z
DTEND:20220203T190000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/65
DESCRIPTION:Title: DT invariants and vertex algebras\nby Sergey Mozgovoy (Trinity Coll
ege (Dublin)) as part of M-seminar\n\n\nAbstract\nCohomological Hall algeb
ras (CoHAs) can be understood as a mathematical incarnation of algebras of
BPS states in string theory. Their Poincare series can be used to determi
ne DT invariants of the corresponding categories.\nFor a symmetric quiver
Q\, the corresponding CoHA is commutative and I will explain how its dual
can be naturally equipped with a structure of a vertex bialgebra. It can a
lso be identified with 1) the universal enveloping algebra of some Lie alg
ebra\, 2) the universal enveloping vertex algebra of some vertex Lie algeb
ra\, 3) the principal free vertex algebra embedded into some lattice verte
x algebra.\nThis identification leads to a new proof of the positivity of
DT invariants. It also allows one to interpret duals of CoHA modules\, ari
sing from moduli spaces of stable framed representations\, as certain subs
paces of principal free vertex algebras.\n
LOCATION:https://researchseminars.org/talk/M-seminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20220207T193000Z
DTEND:20220207T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/66
DESCRIPTION:Title: Quantum Topology at generic q (part 1)\nby Sergei Gukov (Caltech) a
s part of M-seminar\n\n\nAbstract\nThis is the first of a 4-lecture minise
ries.\n\nQuantum topology is a blend of topology and quantum algebra\, whe
re topological invariants of knots and 3-manifolds are constructed from ba
sic building blocks of algebraic origin. The latter\, in turn\, can come f
rom symmetries of solvable lattice models\, from vertex operator algebras\
, from quantum field theories\, and from various constructions in geometri
c representation theory\, thus providing "algebraic bridges" between these
different areas of mathematics and physics. Many invariants of 3-manifold
s --- e.g. the Rokhlin invariant\, Witten-Reshetikhin-Turaev invariants an
d their non-semisimple generalizations (ADO and CGP invariants) --- arise
in this way and involve quantum groups at roots of unity. Constructing q-s
eries invariants associated with quantum groups at generic q requires qual
itatively new techniques. The main goal of these lectures is to offer a sl
ow introduction and a practical guide to these techniques\, illustrated by
many examples and\, hopefully\, led by many questions and suggestions fro
m the audience.\n
LOCATION:https://researchseminars.org/talk/M-seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20220209T193000Z
DTEND:20220209T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/67
DESCRIPTION:Title: Quantum Topology at generic q (part 2)\nby Sergei Gukov (Caltech) a
s part of M-seminar\n\n\nAbstract\nThis is the second of a 4-lecture minis
eries.\n\nQuantum topology is a blend of topology and quantum algebra\, wh
ere topological invariants of knots and 3-manifolds are constructed from b
asic building blocks of algebraic origin. The latter\, in turn\, can come
from symmetries of solvable lattice models\, from vertex operator algebras
\, from quantum field theories\, and from various constructions in geometr
ic representation theory\, thus providing "algebraic bridges" between thes
e different areas of mathematics and physics. Many invariants of 3-manifol
ds --- e.g. the Rokhlin invariant\, Witten-Reshetikhin-Turaev invariants a
nd their non-semisimple generalizations (ADO and CGP invariants) --- arise
in this way and involve quantum groups at roots of unity. Constructing q-
series invariants associated with quantum groups at generic q requires qua
litatively new techniques. The main goal of these lectures is to offer a s
low introduction and a practical guide to these techniques\, illustrated b
y many examples and\, hopefully\, led by many questions and suggestions fr
om the audience.\n
LOCATION:https://researchseminars.org/talk/M-seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20220210T213000Z
DTEND:20220210T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/68
DESCRIPTION:Title: Quantum Topology at generic q (part 3)\nby Sergei Gukov (Caltech) a
s part of M-seminar\n\n\nAbstract\nThis is the third of a 4-lecture minise
ries.\n\nQuantum topology is a blend of topology and quantum algebra\, whe
re topological invariants of knots and 3-manifolds are constructed from ba
sic building blocks of algebraic origin. The latter\, in turn\, can come f
rom symmetries of solvable lattice models\, from vertex operator algebras\
, from quantum field theories\, and from various constructions in geometri
c representation theory\, thus providing "algebraic bridges" between these
different areas of mathematics and physics. Many invariants of 3-manifold
s --- e.g. the Rokhlin invariant\, Witten-Reshetikhin-Turaev invariants an
d their non-semisimple generalizations (ADO and CGP invariants) --- arise
in this way and involve quantum groups at roots of unity. Constructing q-s
eries invariants associated with quantum groups at generic q requires qual
itatively new techniques. The main goal of these lectures is to offer a sl
ow introduction and a practical guide to these techniques\, illustrated by
many examples and\, hopefully\, led by many questions and suggestions fro
m the audience.\n
LOCATION:https://researchseminars.org/talk/M-seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20220211T193000Z
DTEND:20220211T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/69
DESCRIPTION:Title: Quantum Topology at generic q (part 4)\nby Sergei Gukov (Caltech) a
s part of M-seminar\n\n\nAbstract\nThis is the fourth of a 4-lecture minis
eries.\n\nQuantum topology is a blend of topology and quantum algebra\, wh
ere topological invariants of knots and 3-manifolds are constructed from b
asic building blocks of algebraic origin. The latter\, in turn\, can come
from symmetries of solvable lattice models\, from vertex operator algebras
\, from quantum field theories\, and from various constructions in geometr
ic representation theory\, thus providing "algebraic bridges" between thes
e different areas of mathematics and physics. Many invariants of 3-manifol
ds --- e.g. the Rokhlin invariant\, Witten-Reshetikhin-Turaev invariants a
nd their non-semisimple generalizations (ADO and CGP invariants) --- arise
in this way and involve quantum groups at roots of unity. Constructing q-
series invariants associated with quantum groups at generic q requires qua
litatively new techniques. The main goal of these lectures is to offer a s
low introduction and a practical guide to these techniques\, illustrated b
y many examples and\, hopefully\, led by many questions and suggestions fr
om the audience.\n
LOCATION:https://researchseminars.org/talk/M-seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Latyntsev (Oxford University)
DTSTART:20220218T190000Z
DTEND:20220218T200000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/70
DESCRIPTION:Title: Quantum vertex algebras and cohomological Hall algebras\nby Alexei
Latyntsev (Oxford University) as part of M-seminar\n\n\nAbstract\nThere is
an extremely rich history of interaction between string theory and the ma
thematics of moduli spaces\, for instance cohomological Hall algebras/alge
bras of BPS states\, or vertex/chiral algebras.\nIn this talk\, I will exp
lain a link between two of these: Joyce's vertex algebras attached to the
moduli stack of objects in an abelian category\, and one dimensional CoHAs
. This is based on my recent paper 2110.14356\, whose main result says tha
t the cohomologies of such stacks are ``quantum vertex algebras": the fact
orisation/vertex analogues of quasitriangular bialgebras. The main technic
al tool is a ``bivariant" Euler class which makes torus localisation work
in this context. I will discuss applications of these techniques to CoHAs
of coherent sheaves on a curve and future directions.\n
LOCATION:https://researchseminars.org/talk/M-seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitrii Galakhov (IPMU)
DTSTART:20220224T230000Z
DTEND:20220225T000000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/71
DESCRIPTION:Title: Quiver BPS Algebras\nby Dmitrii Galakhov (IPMU) as part of M-semina
r\n\n\nAbstract\nThe quiver Yangian is the algebra underlying BPS state co
unting problems for toric Calabi-Yau three-folds. In this talk I will disc
uss a physical construction of this algebra as it emerges from an effectiv
e quantum field theory (QFT) describing the IR physics of D-branes wrappin
g the three-fold. QFT setup provides as well natural trigonometric and ell
iptic analogues of quiver Yangians\, which could be called toroidal quiver
algebras and elliptic quiver algebras\, respectively. The representations
of the shifted rational\, trigonometric and elliptic algebras can be con
structed in terms of the statistical model of crystal melting. The analysi
s of supersymmetric gauge theories suggests that there exist even richer c
lasses of algebras associated with higher-genus Riemann surfaces and gener
alized cohomology theories.\nIf time permits\, I would mention possible de
velopments and relations to (possibly novel) integrable models.\nThis talk
is based on arXiv:2008.07006\, arXiv:2106.01230\, arXiv:2108.10286.\n
LOCATION:https://researchseminars.org/talk/M-seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Voronov (University of Minnesota)
DTSTART:20220310T213000Z
DTEND:20220310T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/72
DESCRIPTION:Title: Mysterious Triality\nby Alexander Voronov (University of Minnesota)
as part of M-seminar\n\n\nAbstract\nMysterious duality was discovered by
Iqbal\, Neitzke\, and Vafa in 2002 as a convincing\, yet mysterious corres
pondence between certain symmetry patterns in toroidal compactifications o
f M-theory and del Pezzo surfaces\, both governed by the root system serie
s E_k. It turns out that the sequence of del Pezzo surfaces is not the onl
y sequence of objects in mathematics which gives rise to the same E_k symm
etry pattern. I will present a sequence of topological spaces\, starting w
ith the four-sphere S^4\, and then forming its iterated cyclic loop spaces
L_c^k S^4\, within which we will see the E_k symmetry pattern via rationa
l homotopy theory. For this sequence of spaces\, the correspondence betwee
n its E_k symmetry pattern and that of toroidal compactifications of M-the
ory is no longer a mystery\, as each space L_c^k S^4 is naturally related
to the compactification of M-theory on the k-torus via identification of t
he equations of motion of (11-k)-dimensional supergravity as the defining
equations of the Sullivan minimal model of L_c^k S^4. This gives an explic
it duality between rational homotopy theory and physics. Thereby\, Iqbal\,
Neitzke\, and Vafa’s mysterious duality between algebraic geometry and
physics is extended to a triality involving algebraic topology\, with the
duality between topology and physics made explicit\, i.e.\, demystified. T
he mystery is now transferred to the mathematical realm as duality between
algebraic geometry and algebraic topology. This is a report on а recent
work\, arXiv:2111.14810 [hep-th]\, with
Hisham Sati.\n
LOCATION:https://researchseminars.org/talk/M-seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Gorsky (UC Davis)
DTSTART:20220303T213000Z
DTEND:20220303T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/73
DESCRIPTION:Title: Algebraic weaves and braid varieties\nby Evgeny Gorsky (UC Davis) a
s part of M-seminar\n\n\nAbstract\nIn the talk I will define braid varieti
es\, a class of affine algebraic varieties associated to positive braids\,
and explain their relation to Richardson and positroid varieties\, HOMFLY
polynomial and Khovanov-Rozansky homology. I will also develop a Soergel-
like diagrammatic calculus for correspondences between the braid varieties
. This is a joint work with Roger Casals\, Mikhail Gorsky and Jose Siment
al Rodriguez.\n
LOCATION:https://researchseminars.org/talk/M-seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics\, SDU)
DTSTART:20220321T183000Z
DTEND:20220321T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/74
DESCRIPTION:Title: Quadratic differentials\, stability conditions\, and DT invariants\, le
cture 1\nby Fabian Haiden (Center for Quantum Mathematics\, SDU) as pa
rt of M-seminar\n\n\nAbstract\nLecture 1: Quadratic differentials\, Fukaya
categories of surfaces\, and stability conditions\n\nCombining ideas from
string theory and geometric invariant theory\, Bridgeland introduced the
notion of a stability condition on a triangulated category. Since then\, t
he problem of determining the structure of spaces of all stability conditi
ons on triangulated categories\, which are complex analytic manifolds\, ha
s proven to be quite challenging and has only been solved in a handful of
examples. In some cases though\, spaces of stability conditions turn out t
o have a very concrete and geometric interpretation as spaces of quadratic
differentials\, or equivalently flat surfaces - objects of intense study
in ergodic theory. In these cases\, the triangulated category is the (part
ially wrapped) Fukaya category of a surface. However\, one can also instea
d consider certain 3-d Calabi-Yau triangulated categories\, and this is ne
cessary to make contact with the theory of motivic Donaldson-Thomas invari
ants of Kontsevich-Soibelman. As an application one obtains wall-crossing
formulas for counts of finite-length geodesics on flat surfaces.\nThis lec
ture series will be based on arXiv:1409.8611\, arXiv:2104.06018\, as well
as unpublished work. The aim will be to present a unified picture of exist
ing results as well as indicate open questions and future directions of re
search.\n
LOCATION:https://researchseminars.org/talk/M-seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics\, SDU)
DTSTART:20220323T183000Z
DTEND:20220323T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/75
DESCRIPTION:Title: Quadratic differentials\, stability conditions\, and DT invariants\, le
cture 2\nby Fabian Haiden (Center for Quantum Mathematics\, SDU) as pa
rt of M-seminar\n\n\nAbstract\nLecture 2: Calabi-Yau categories of surface
s\n\nCombining ideas from string theory and geometric invariant theory\, B
ridgeland introduced the notion of a stability condition on a triangulated
category. Since then\, the problem of determining the structure of spaces
of all stability conditions on triangulated categories\, which are comple
x analytic manifolds\, has proven to be quite challenging and has only bee
n solved in a handful of examples. In some cases though\, spaces of stabil
ity conditions turn out to have a very concrete and geometric interpretati
on as spaces of quadratic differentials\, or equivalently flat surfaces -
objects of intense study in ergodic theory. In these cases\, the triangula
ted category is the (partially wrapped) Fukaya category of a surface. Howe
ver\, one can also instead consider certain 3-d Calabi-Yau triangulated ca
tegories\, and this is necessary to make contact with the theory of motivi
c Donaldson-Thomas invariants of Kontsevich-Soibelman. As an application o
ne obtains wall-crossing formulas for counts of finite-length geodesics on
flat surfaces.\nThis lecture series will be based on arXiv:1409.8611\, ar
Xiv:2104.06018\, as well as unpublished work. The aim will be to present a
unified picture of existing results as well as indicate open questions an
d future directions of research.\n
LOCATION:https://researchseminars.org/talk/M-seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics\, SDU)
DTSTART:20220324T183000Z
DTEND:20220324T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/76
DESCRIPTION:Title: Quadratic differentials\, stability conditions\, and DT invariants\, le
cture 3\nby Fabian Haiden (Center for Quantum Mathematics\, SDU) as pa
rt of M-seminar\n\n\nAbstract\nLecture 3: DT-invariants and wall-crossing
for quadratic differentials\n\nCombining ideas from string theory and geom
etric invariant theory\, Bridgeland introduced the notion of a stability c
ondition on a triangulated category. Since then\, the problem of determini
ng the structure of spaces of all stability conditions on triangulated cat
egories\, which are complex analytic manifolds\, has proven to be quite ch
allenging and has only been solved in a handful of examples. In some cases
though\, spaces of stability conditions turn out to have a very concrete
and geometric interpretation as spaces of quadratic differentials\, or equ
ivalently flat surfaces - objects of intense study in ergodic theory. In t
hese cases\, the triangulated category is the (partially wrapped) Fukaya c
ategory of a surface. However\, one can also instead consider certain 3-d
Calabi-Yau triangulated categories\, and this is necessary to make contact
with the theory of motivic Donaldson-Thomas invariants of Kontsevich-Soib
elman. As an application one obtains wall-crossing formulas for counts of
finite-length geodesics on flat surfaces.\nThis lecture series will be bas
ed on arXiv:1409.8611\, arXiv:2104.06018\, as well as unpublished work. Th
e aim will be to present a unified picture of existing results as well as
indicate open questions and future directions of research.\n
LOCATION:https://researchseminars.org/talk/M-seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Koroteev (UC Berkeley and Rutgers University)
DTSTART:20220331T203000Z
DTEND:20220331T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/77
DESCRIPTION:Title: q-Opers — what they are and what are they good for?\nby Peter Kor
oteev (UC Berkeley and Rutgers University) as part of M-seminar\n\n\nAbstr
act\nI will introduce the new geometric object - (G\,q)-opers on a Rieman
n surface where G is a simple simply connected Lie algebra. I will describ
e their applications in geometric Langlands and integrable systems. Using
the formalism of (G\,q)-opers we can describe spectrum of quantum integrab
le models\, like XXZ spin chains and their generalizations in representati
on theory (so called quantum/classical duality). As a different applicatio
n we can study wall crossing transformations between fundamental solutions
of Fuchsian ODEs with regular singularities (ODE/IM correspondence) using
(G\,q)-oper connections.\n
LOCATION:https://researchseminars.org/talk/M-seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Losev (Yale University)
DTSTART:20220408T203000Z
DTEND:20220408T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/78
DESCRIPTION:Title: Harish-Chandra modules and quantizations\nby Ivan Losev (Yale Unive
rsity) as part of M-seminar\n\n\nAbstract\nLet G be a complex semisimple a
lgebraic group\, g its Lie algebra and K a symmetric subgroup of G. In thi
s situation one can talk about Harish-Chandra (g\,K)-modules. Their study
is a classical chapter of Lie representation theory\, largely motivated by
the study of representations of semisimple real groups and\, in particula
r\, the classification of unitary representations. It is classically expec
ted that Harish-Chandra modules arising from the latter are related to qua
ntizations of nilpotent orbits and their covers. In the recent years\, the
re has been a lot of progress understanding the latter that in particular
shed some light on the geometric classification of certain classes of Hari
sh-Chandra modules that should come from unitary representations. I will s
urvey some of this progress in my talk. Based on the joint work with Mason
-Brown and Matvieievskyi\, arXiv:2108.03453 .\n
LOCATION:https://researchseminars.org/talk/M-seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Sheridan (University of Edinburgh)
DTSTART:20220422T203000Z
DTEND:20220422T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/79
DESCRIPTION:Title: Quantum cohomology as a deformation of symplectic cohomology\nby Ni
ck Sheridan (University of Edinburgh) as part of M-seminar\n\n\nAbstract\n
Let X be a compact symplectic manifold\, and D a normal crossings symplect
ic divisor in X. We give a criterion under which the quantum cohomology of
X is the cohomology of a natural deformation of the symplectic cochain co
mplex of X \\ D. The criterion can be thought of in terms of the Kodaira d
imension of X (which should be non-positive)\, and the log Kodaira dimensi
on of X \\ D (which should be non-negative). We will discuss applications
to mirror symmetry. This is joint work with Strom Borman and Umut Varolgun
es.\n
LOCATION:https://researchseminars.org/talk/M-seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART:20220414T203000Z
DTEND:20220414T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/80
DESCRIPTION:Title: Cohomology and intersection theory on stacks\nby Adeel Khan (Academ
ia Sinica) as part of M-seminar\n\n\nAbstract\nI will give an overview of
some recent work on extending cohomological and intersection-theoretic met
hods to stacks. This formalism subsumes equivariant intersection theory i
n the sense of Edidin-Graham and also incorporates virtual phenomena via a
derived version of specialization to the normal cone. I will also discus
s a very general new localization theorem for stacks which recovers Atiyah
-Bott localization in the case of quotients by torus actions. Finally\, I
will explain a categorification of this story\, involving a derived micro
localization functor for constructible sheaves\, which is closely connecte
d with categorified Donaldson-Thomas theory. The localization theorem is
joint with Aranha\, Latyntsev\, Park and Ravi\, and the applications to DT
theory are joint with Kinjo.\n
LOCATION:https://researchseminars.org/talk/M-seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Doan (Columbia & Trinity College\, Cambridge)
DTSTART:20220428T203000Z
DTEND:20220428T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/81
DESCRIPTION:Title: Holomorphic Floer theory and the Fueter equation\nby Aleksander Doa
n (Columbia & Trinity College\, Cambridge) as part of M-seminar\n\n\nAbstr
act\nI will discuss an idea of constructing a category associated with a p
air of holomorphic Lagrangians in a hyperkahler manifold\, or\, more gener
ally\, a manifold equipped with a triple of almost complex structures I\,J
\,K satisfying the quaternionic relation IJ =-JI= K. This category can be
seen as an infinite-dimensional version of the Fukaya-Seidel category asso
ciated with a Lefschetz fibration. While many analytic aspects of this pro
posal remain unexplored\, I will argue that in the case of the cotangent b
undle of a Lefschetz fibration\, our construction recovers the Fukaya-Seid
el category. This talk is based on joint work with Semon Rezchikov\, and b
uilds on earlier ideas of Haydys\, Gaiotto-Moore-Witten\, and Kapranov-Kon
tsevich-Soibelman.\n
LOCATION:https://researchseminars.org/talk/M-seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Kivinen (EPFL)
DTSTART:20220505T173000Z
DTEND:20220505T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/82
DESCRIPTION:Title: Weight polynomials of compactified Jacobians and link invariants\nb
y Oscar Kivinen (EPFL) as part of M-seminar\n\n\nAbstract\nUsing a recursi
ve algorithm for orbital integrals of tamely ramified elliptic elements in
p-adic GL_n\, we compute the weight polynomials of (local) compactified J
acobians of planar curves. Depending on one's taste\, these can be also in
terpreted as point-counts on Hitchin fibers or affine Springer fibers in t
ype A. The algorithm is based on old work of Waldspurger and can be interp
reted using an action of the affine Yangian of gl(1) on the Fock space\, w
here it becomes clear that there is a relationship to knot invariants of H
OMFLY type. This also proves a virtual version of the Cherednik-Danilenko
conjecture on Betti numbers of Jacobian factors.\nIn fact\, the algorithm
yields more\, such as so called Shalika germs for the elements in question
. These have a geometric interpretation on the Hilbert scheme of points on
C^2\, which I will also discuss. This is joint work with Cheng-Chiang Tsa
i.\n
LOCATION:https://researchseminars.org/talk/M-seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiro Lee Tanaka (Texas State University)
DTSTART:20220922T203000Z
DTEND:20220922T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/83
DESCRIPTION:Title: Stable Weinstein geometry through localizations\nby Hiro Lee Tanaka
(Texas State University) as part of M-seminar\n\n\nAbstract\nMuch of comp
utational math is formula-driven\, while much of categorical math is forma
lism-driven. Mirror symmetry is rich in part because many of its results a
re driven by both. With the advent of stable-homotopy-theoretic invariants
in symplectic geometry\, there has been a real need for better-behaved fo
rmalisms in symplectic geometry. In this talk\, we will talk about recent
success in constructing the formalism\, especially in the setting of certa
in non-compact symplectic manifolds called Weinstein sectors. The results
have concrete geometric consequences\, like showing that spaces of embeddi
ngs of these manifolds map continuously to spaces of maps between certain
invariants. (And in particular\, leads to higher-homotopy-group generaliza
tions\, in the Weinstein setting\, of the Seidel homomorphism\, similar to
works of Savelyev and Oh-Tanaka.) The main result we'll discuss is that t
he infinity-category of stabilized sectors can be constructed using the ca
tegorically formal process of localization. Most of what we discuss is joi
nt with Oleg Lazarev and Zachary Sylvan.\n
LOCATION:https://researchseminars.org/talk/M-seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Pomerleano (University of Massachusetts Boston)
DTSTART:20221007T203000Z
DTEND:20221007T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/84
DESCRIPTION:Title: Singularities of the quantum connection on a Fano variety\nby Danie
l Pomerleano (University of Massachusetts Boston) as part of M-seminar\n\n
\nAbstract\nThe small quantum connection on a Fano variety is one of the s
implest objects in enumerative geometry. Nevertheless\, it is the subject
of far-reaching conjectures known as the Dubrovin/Gamma conjectures. Tradi
tionally\, these conjectures are made for manifolds with semi-simple quant
um cohomology or more generally for Fano manifolds whose quantum connectio
n is of unramified exponential type at $q=\\infty$. I will explain a progr
am\, joint with Paul Seidel\, to show that this unramified exponential typ
e property holds for all Fano manifolds M carrying a smooth anticanonical
divisor D. The basic idea of our argument is to view these structures thro
ugh the lens of a noncommutative Landau-Ginzburg model intrinsically attac
hed to (M\,D).\n
LOCATION:https://researchseminars.org/talk/M-seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Soibelman (IHES)
DTSTART:20221013T173000Z
DTEND:20221013T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/85
DESCRIPTION:Title: Quantized integrable systems\, normal forms\, and variation of Hodge st
ructures\nby Alexander Soibelman (IHES) as part of M-seminar\n\n\nAbst
ract\nA classical theorem due to Birkhoff states that on a complex symplec
tic manifold a function near its Morse critical point can be transformed b
y a formal symplectomorphism into a normal form given by a power series in
the pairwise sums of squares of the coordinates. Using a quantum analog o
f this normal form\, one can compute the eigenvalues of the Schrödinger o
perator\, given certain conditions. In my talk\, I will explain how to obt
ain the Birkhoff normal form of a quantum Hamiltonian geometrically\, rela
ting it to the quantization of integrable systems and to formal deformatio
ns of variations of Hodge structures. This is joint work in progress with
Maxim Kontsevich.\n
LOCATION:https://researchseminars.org/talk/M-seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Hilburn (Perimeter Institute)
DTSTART:20221020T203000Z
DTEND:20221020T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/86
DESCRIPTION:Title: Towards 2-Categorical 3d Mirror Symmetry\nby Justin Hilburn (Perime
ter Institute) as part of M-seminar\n\n\nAbstract\nBy now it is known that
many interesting phenomena in geometry and representation theory can be u
nderstood as aspects of mirror symmetry of 3d N=4 SUSY QFTs. Such a QFT is
associated to a hyper-Kähler manifold X equipped with a hyper-Hamiltonia
n action of a compact Lie group G and admits two topological twists. The f
irst twist\, which is known as the 3d B-model or Rozansky-Witten theory\,
is a TQFT of algebro-geometric flavor and has been studied extensively by
Kapustin\, Rozansky and Saulina. The second twist\, which is known as the
3d A-model or 3d Seiberg-Witten theory\, is a more mysterious TQFT of symp
lecto-topological flavor. In this talk I will discuss what is known about
the 2-categories of boundary conditions for these two TQFTs. They are expe
cted to provide two distinct categorifications of category O for the hyper
kahler quotient X///G and 3d mirror symmetry is expected to induce a categ
orification of the Koszul duality between categories O for mirror symplect
ic resolutions. For abelian gauge theories this picture is work in progres
s with Ben Gammage and Aaron Mazel-Gee. This generalizes the works of Kapu
stin-Vyas-Setter and Teleman on pure gauge theory.\n
LOCATION:https://researchseminars.org/talk/M-seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Bridgeland (University of Sheffield)
DTSTART:20221027T150000Z
DTEND:20221027T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/87
DESCRIPTION:Title: Geometry from Donaldson-Thomas invariants\nby Tom Bridgeland (Unive
rsity of Sheffield) as part of M-seminar\n\n\nAbstract\nOur general aim is
to use the Donaldson-Thomas invariants of a 3-Calabi-Yau triangulated ca
tegory to define a geometric structure on its space of stability condition
s. So far we only understand how to do this in a few classes of examples.
In the talk I'll explain (i) the geometry we expect to obtain (which invol
ves a hyperkahler structure)\, and (ii) a moduli-theoretic construction of
this geometry in the case of "categories of class S[A_1]" (where the stab
ility space parameterises algebraic curves equipped with quadratic differe
ntials).\n
LOCATION:https://researchseminars.org/talk/M-seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadij Bojko (ETH Zurich)
DTSTART:20221103T190000Z
DTEND:20221103T200000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/88
DESCRIPTION:Title: Wall-crossing for Calabi-Yau fourfolds and applications\nby Arkadij
Bojko (ETH Zurich) as part of M-seminar\n\n\nAbstract\nThere are multiple
existing theories studying wall-crossing of sheaf-counting invariants in
dimensions less than or equal to three. Recently these invariants were als
o extended to Calabi-Yau fourfolds where it was reasonable to ask about an
analogous story. I will explain the framework leading to the wall-crossin
g formulae proposed by Joyce and describe their proof. The main goal of th
is project is the proof of existing conjectures relating different stable
pairs counting points\, curves and surfaces in Calabi-Yau fourfolds. For e
xample\, it proves my previous computations for Hilbert schemes of points.
\n
LOCATION:https://researchseminars.org/talk/M-seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanki Lekili (Imperial College London)
DTSTART:20221201T160000Z
DTEND:20221201T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/89
DESCRIPTION:Title: Equivariant Fukaya categories at the singular value\nby Yanki Lekil
i (Imperial College London) as part of M-seminar\n\n\nAbstract\nWe have so
me new conjectures and examples where we relate wrapped Fukaya categories
of symplectic manifolds with Hamiltonian S^1 actions and the wrapped Fukay
a categories of their Hamiltonian reductions.\nJoint work with Ed Segal.\n
LOCATION:https://researchseminars.org/talk/M-seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20221110T193000Z
DTEND:20221110T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/90
DESCRIPTION:Title: Affine BPS algebras and W algebras\nby Ben Davison (University of E
dinburgh) as part of M-seminar\n\n\nAbstract\nOne may associate to a quive
r Q with potential W a certain Lie algebra\, called the BPS Lie algebra.
On the one hand this Lie algebra generates the Kontsevich-Soibelman cohomo
logical Hall algebra (CoHA) associated to Q and W under a Yangian-type PBW
theorem\, and on the other hand it partially categorifies the BPS invaria
nts of the Jacobi algebra associated to (Q\,W). For special choices of (Q
\,W)\, the resulting cohomological Hall algebra is isomorphic to the cohom
ological Hall algebra studied by Schiffamnn and Vasserot in their solution
of the AGT conjecture.\nI will explain how a special case of a joint resu
lt with Kinjo enables us to affinize the BPS Lie algebra for these CoHAs\,
and express the CoHA as a universal enveloping algebra. I will explain h
ow for the three-loop quiver with its canonical cubic potential\, a one-pa
rameter deformation of the affine BPS Lie algebra recovers one half of the
Lie algebra of differential operators on the complex torus. In particula
r\, this implies that the associated CoHA is spherically generated\, so th
at we can use a result of Rapčák\, Soibelman\, Yang and Zhou to complete
ly describe the fully deformed version of this algebra in terms of half of
the affine Yangian of gl(1).\n
LOCATION:https://researchseminars.org/talk/M-seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Schiffmann (Université de Paris-Sud ORSAY)
DTSTART:20221118T150000Z
DTEND:20221118T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/91
DESCRIPTION:Title: COHA of zero dimensional sheaves on surfaces and the P=W conjecture
\nby Olivier Schiffmann (Université de Paris-Sud ORSAY) as part of M-semi
nar\n\n\nAbstract\nCohomological Hall algebras of 2CY categories feature i
n several recent geometric constructions of infinite dimensional quantum g
roups (such as affine Yangians) and their representations. The case of zer
o dimensional sheaves on smooth surfaces (such as projective surfaces\, or
line bundles over smooth projective curves) has attracted particular atte
ntion due to the analogy with usual Hecke operators (acting on moduli spac
es of sheaves on curves as opposed to surfaces). We will describe the COHA
in this case (a joint work with Mellit\, Minets and Vasserot)\, and we wi
ll sketch its use in a recent proof of the P=W conjecture of de Catlado\,
Hausel and Migliorini relating the Hodge structure of character varieties
and the perverse cohomology of the Hitchin fiibration (a joint work with H
ausel\, Mellit and Minets).\n
LOCATION:https://researchseminars.org/talk/M-seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lino Amorim (Kansas State University)
DTSTART:20230201T213000Z
DTEND:20230201T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/92
DESCRIPTION:Title: Enumerative invariants from categories\nby Lino Amorim (Kansas Stat
e University) as part of M-seminar\n\n\nAbstract\nKontsevich suggested tha
t enumerative predictions of Mirror Symmetry should follow directly from H
omological Mirror Symmetry. This requires a natural construction of analog
ues of Gromov-Witten invariants associated to any dg or A-infinity Calabi-
Yau category (with some extra choices). I will discuss two approaches to t
his construction: 1) categorical primitive forms\, a non-commutative versi
on of Saito's theory of primitive forms for singularities\, which gives on
ly genus zero invariants\; 2) Costello's enumerative invariants which conj
ecturally give invariants in all genera.\n
LOCATION:https://researchseminars.org/talk/M-seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semon Rezchikov (IAS/Princeton University)
DTSTART:20230209T213000Z
DTEND:20230209T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/93
DESCRIPTION:Title: Categorical aspects of the Fueter Equation\nby Semon Rezchikov (IAS
/Princeton University) as part of M-seminar\n\n\nAbstract\nThe (3d) Fueter
equation is the three-dimensional analog of the pseudoholomorphic map equ
ation\, and as such underlies a three-dimensional topological quantum fiel
d theory. This PDE underlies the mathematics of the A-type twist of the 3D
N=4 sigma model\, which has a hyperkahler manifold as its target. One can
think of this topological quantum field theory as a simultaneous complexi
fication and categorification of the Fukaya category\; in particular\, it
assigns to a ("weak") hyperkahler manifold a 2-category with objects holom
orphic Lagrangians\, which in an appropriate sense categorifies the Fukaya
category. Certain basic open problems remain about the analysis of the Fu
eter equation\, but this categorical viewpoint suggests new tractable dire
ctions in the differential geometry of this equation. In particular\, just
as holomorphic strips between nearby Lagrangans are in bijection with Mor
se trajectories of a real morse function\, Fueter maps between nearby holo
morphic Lagrangians are in bijection with complex gradient trajectories of
a holomorphic morse function\, also known as zeta-instantons. Thus\, in t
he (A-twist) Fueter 2-category\, hom-categories are locally modeled on Fuk
aya-Seidel categories\, just as in the B-twist Kapustin-Rozansky-Saulinas
category\, hom-categories are locally modeled on matrix factorization cate
gories. Categorical 3D mirror symmetry should exchange these pairs of 2-ca
tegories associated to pairs of 3d mirror manifolds. I will survey these i
deas and describe interesting directions and puzzles in this story. This i
s based on joint work with Aleksander Doan\, as well as on discussions wit
h Justin Hilburn and Benjamin Gammage.\n
LOCATION:https://researchseminars.org/talk/M-seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Danilenko (UC Berkeley)
DTSTART:20230216T213000Z
DTEND:20230216T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/94
DESCRIPTION:Title: Stable envelopes from 2d mirror symmetry\nby Ivan Danilenko (UC Ber
keley) as part of M-seminar\n\n\nAbstract\nHomological mirror symmetry pre
dicts an equivalence between the derived category of equivariant coherent
sheaves on the additive Coulomb branch X and a version of the wrapped Fuka
ya category on multiplicative Coulomb branch Y with superpotential W. If o
ne decategorifies both sides by taking K-theory\, the construction still g
ives an interesting identification between well-known objects in the equiv
ariant K-theory of X and cycles with coefficients in local systems on Y. T
he talk will show how it works for the fixed point basis and the stable en
velopes. Work in progress with Andrey Smirnov\, with many insights from th
e joint project with Mina Aganagic\, Peng Zhou and Yixuan Li.\n
LOCATION:https://researchseminars.org/talk/M-seminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Reshetikhin (UC Berkeley and BIMSA)
DTSTART:20230223T213000Z
DTEND:20230223T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/95
DESCRIPTION:Title: Solitons in infinite relativistic Toda system\nby Nicolai Reshetikh
in (UC Berkeley and BIMSA) as part of M-seminar\n\n\nAbstract\nThis system
is a "relativistic" generalization of the infinite Toda chain. In is a $G
L(\\infty)$ version of the Toda-Coxeter system for $SL(N)$ with the standa
rd Poisson Lie structure. The phase space of this system is an example of
an infinite cluster variety. Assuming an analog of rapidly decaying bounda
ry conditions we construct soliton solutions for both\, factorization disc
rete time dynamics and for continuous time integrable dynamics. We also co
nstruct action-angle variables from scattering data. This is a joint work
with Cory Lansford.\n
LOCATION:https://researchseminars.org/talk/M-seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoel Groman (Hebrew University)
DTSTART:20230302T213000Z
DTEND:20230302T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/96
DESCRIPTION:Title: The closed string mirror construction\nby Yoel Groman (Hebrew Unive
rsity) as part of M-seminar\n\n\nAbstract\nConsider a 2n-dimensional sympl
ectic Calabi Yau manifold equipped with a Maslov 0 Lagrangian torus fibrat
ion with singularities over a base B. According to modern interpretations
of the SYZ conjecture\, there should be an associated analytic mirror vari
ety with a non Archimedean torus fibration over B. I will suggest a genera
l construction called the closed string mirror which is based on relative
symplectic cohomologies of the fibers. A priori the closed string mirror i
s only a set with a map to the base. I will discuss work in progress on so
me general hypotheses for when it is in fact an n-dimensional rigid analyt
ic variety with a non Archimedean torus fibration. I will touch on the rel
ation to enumerative and homological mirror symmetry.\n
LOCATION:https://researchseminars.org/talk/M-seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Mellit (University of Vienna)
DTSTART:20230309T160000Z
DTEND:20230309T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/97
DESCRIPTION:Title: P=W via H_2\nby Anton Mellit (University of Vienna) as part of M-se
minar\n\n\nAbstract\nBy $H_2$ we denote the Lie algebra of polynomial hami
ltonian vector fields on the plane. We consider the moduli space of stable
twisted Higgs bundles on an algebraic curve of given coprime rank and deg
ree. De Cataldo\, Hausel and Migliorini proved in the case of rank 2 and c
onjectured in arbitrary rank that two natural filtrations on the cohomolog
y of the moduli space coincide. One is the weight filtration W coming from
the Betti realization\, and the other one is the perverse filtration P in
duced by the Hitchin map. Motivated by computations of the Khovanov-Rozans
ky homology of links by Gorsky\, Hogancamp and myself\, we look for an act
ion of $H_2$ on the cohomology of the moduli space. We find it in the alge
bra generated by two kinds of natural operations: on the one hand we have
the operations of cup product by tautological classes\, and on the other h
and we have the Hecke operators acting via certain correspondences. We the
n show that both P and W coincide with the filtration canonically associat
ed to the $sl_2$ subalgebra of $H_2$. Based on joint work with Hausel\, Mi
nets and Schiffmann.\n
LOCATION:https://researchseminars.org/talk/M-seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Moreira (ETH)
DTSTART:20230323T203000Z
DTEND:20230323T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/98
DESCRIPTION:Title: Virasoro constraints in sheaf theory\nby Miguel Moreira (ETH) as pa
rt of M-seminar\n\n\nAbstract\nVirasoro constraints for Gromov-Witten inva
riants have a rich history tied to the very beginning of the subject\, but
recently there have been many developments on the sheaf side. In this tal
k I will survey those developments and talk about joint work with A. Bojko
and W. Lim where we propose a general conjecture of Virasoro constraints
for moduli spaces of sheaves and formulate it using the vertex algebra tha
t D. Joyce recently introduced to study wall-crossing. Using Joyce's frame
work we can show compatibility between wall-crossing and the constraints\,
which we then use to prove that they hold for moduli of stable sheaves on
curves and surfaces with h^0\,1=h^0\,2=0.\n
LOCATION:https://researchseminars.org/talk/M-seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Gammage (Harvard University)
DTSTART:20230330T203000Z
DTEND:20230330T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/99
DESCRIPTION:Title: Structural features of 3d mirror symmetry\nby Benjamin Gammage (Har
vard University) as part of M-seminar\n\n\nAbstract\n"Homological" 3d mirr
or symmetry is an equivalence between the Kapustin-Rozansky-Saulina 2-cate
gory and an as-yet-undefined "Fukaya-Fueter" 2-category associated to dual
holomorphic symplectic stacks. Many statements\, some classical and some
new\, may be recovered from such an equivalence by decategorification. We
will discuss what is known in the toric setting\, where decategorification
can be used to produce both the Braden-Licata-Proudfoot-Webster hypertori
c Koszul duality and a geometric version of Tate's thesis. This is based o
n joint work with Justin Hilburn & Aaron Mazel-Gee.\n
LOCATION:https://researchseminars.org/talk/M-seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (Bogazici University)
DTSTART:20230407T160000Z
DTEND:20230407T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/100
DESCRIPTION:Title: Mirror formal schemes of symplectic manifolds equipped with generalize
d cut decompositions\nby Umut Varolgunes (Bogazici University) as part
of M-seminar\n\n\nAbstract\nI will discuss the notion of generalized Delz
ant subdomains of graded symplectic manifolds and their relative symplecti
c cohomology. Assuming that we have an involutive decomposition into such
domains\, I will construct a mirror formal scheme over the Novikov ring. T
he key is to be able to compute the invariants modulo Thbar\, where hbar i
s a positive constant depending on the decomposition\, finiteness of bound
ary depth which leads to homology level completeness and an injectivity st
atement mirror to uniqueness of analytic continuation. Then I will assume
the existence of a "homological section" and construct the HMS functor. I
will end by discussing when one should expect this functor to be cohomolog
ically full and faithful via the notion of local generation.\n
LOCATION:https://researchseminars.org/talk/M-seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (University of Georgia)
DTSTART:20230413T203000Z
DTEND:20230413T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/101
DESCRIPTION:Title: Quivers\, flow trees and log curves\nby Pierrick Bousseau (Univers
ity of Georgia) as part of M-seminar\n\n\nAbstract\nDonaldson-Thomas (DT)
invariants of a quiver with potential can be expressed in terms of simpler
attractor DT invariants by a universal formula. The coefficients in this
formula are calculated combinatorially using attractor flow trees. In join
t work with Arguz (arXiv:2302.02068)\, we prove that these coefficients ar
e genus 0 log Gromov--Witten invariants of d-dimensional toric varieties\,
where d is the number of vertices of the quiver. This result follows from
a log-tropical correspondence theorem which relates (d-2)-dimensional fam
ilies of tropical curves obtained as universal deformations of attractor f
low trees\, and rational log curves in toric varieties.\n
LOCATION:https://researchseminars.org/talk/M-seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Hugtenburg (University of Edinburgh)
DTSTART:20230420T170000Z
DTEND:20230420T180000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/102
DESCRIPTION:Title: Gromov-Witten invariants from the Fukaya category\nby Kai Hugtenbu
rg (University of Edinburgh) as part of M-seminar\n\n\nAbstract\nThis talk
will report on recent progress on obtaining (open) Gromov-Witten invarian
ts from the Fukaya category. A crucial ingredient is showing that the cycl
ic open-closed map\, which maps the cyclic homology of the Fukaya category
of X to its S1-equivariant quantum cohomology\, respects connections. Alo
ng the way we will encounter R-matrices\, which were used in the Givental-
Teleman classification of semisimple cohomological field theories\, and al
low one to determine higher genus Gromov-Witten invariants from genus 0 in
variants. I will then present some evidence that this approach might exten
d beyond the semisimple case. Time permitting\, I will explain how one can
extend these results to obtain open Gromov-Witten invariants from the Fuk
aya category.\n
LOCATION:https://researchseminars.org/talk/M-seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Diaconescu (Rutgers University)
DTSTART:20230427T170000Z
DTEND:20230427T180000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/103
DESCRIPTION:Title: Flops and Hilbert scheme of space curve singularities\nby Emanuel
Diaconescu (Rutgers University) as part of M-seminar\n\n\nAbstract\nThis i
s joint work with Mauro Porta\, Francesco Sala and Arian Vosoughinia using
pagoda flop transitions in order to derive explicit results for topologic
al invariants of Hilbert schemes of space curve singularities.\n
LOCATION:https://researchseminars.org/talk/M-seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilia Itenberg (Sorbonne University)
DTSTART:20230504T160000Z
DTEND:20230504T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/104
DESCRIPTION:Title: Empty real plane sextic curves\nby Ilia Itenberg (Sorbonne Univers
ity) as part of M-seminar\n\n\nAbstract\nMany geometric questions about K3
-surfaces can be restated and solved in purely arithmetical terms\, by mea
ns of an appropriately defined homological type. For example\, this works
well in the study of singular complex sextic curves or quartic surfaces\,
as well as in that of smooth real ones. However\, when the two are combine
d (singular real curves or surfaces)\, the approach fails as the natural c
oncept of homological type does not fully reflect the geometry. We show th
at the situation can be repaired if the curves in question have empty real
part\; then\, one can confine oneself to the homological types consisting
of the exceptional divisors\, polarization\, and real structure. The resu
lting arithmetical problem can be solved\, and this leads to an equivarian
t equisingular deformation classification of real plane sextics with empty
real part. This is a joint work with Alex Degtyarev.\n
LOCATION:https://researchseminars.org/talk/M-seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT)
DTSTART:20230921T211500Z
DTEND:20230921T221500Z
DTSTAMP:20260315T025116Z
UID:M-seminar/105
DESCRIPTION:Title: On Springer theory for homogeneous affine Springer fibers\nby Roma
n Bezrukavnikov (MIT) as part of M-seminar\n\n\nAbstract\nSpringer fibers
are subvarieties in the flag variety of a reductive group playing a key ro
le in geometric representation theory. One of their important features is
that they arise as central Lagrangian fibers of a symplectic resolution of
a singular space known as the Slodowy slice. Affine Springer fibers are l
oop group analogues of the Springer fibers\, they are closely related to s
ingular fibers of the Hitchin integrable system. In a joint work with Pabl
o Boixeda-Alvarez\, Michael McBreen and Zhiwei Yun we construct the analog
ue of a Slodowy slice for some (namely\, homogeneous) affine Springer fibe
rs. The construction is based on a version of the Hitchin space involving
connections with an irregular singularity. Time permitting\, I will mentio
n applications to quantum groups at a root of unity etc.\n
LOCATION:https://researchseminars.org/talk/M-seminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Liu (IPMU)
DTSTART:20230928T230000Z
DTEND:20230929T000000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/106
DESCRIPTION:Title: The K-theoretic DT/PT vertex correspondence\nby Henry Liu (IPMU) a
s part of M-seminar\n\n\nAbstract\nOn smooth quasi-projective toric 3- and
4-folds\, vertices are the contributions from an affine toric chart to th
e enumerative invariants of Donaldson-Thomas (DT) or Pandharipande-Thomas
(PT) moduli spaces. Unlike partition functions\, vertices are fundamentall
y torus-equivariant objects\, and they carry a great deal of combinatorial
complexity\, particularly in equivariant K-theory. In joint work with Nic
k Kuhn and Felix Thimm\, we give two different proofs of the K-theoretic 3
-fold DT/PT vertex correspondence. Both proofs use equivariant wall-crossi
ng in a setup originally due to Toda\; one uses a Mochizuki-style master s
pace\, while the other uses ideas from Joyce's recent universal wall-cross
ing machine. A crucial new ingredient is the construction of *symmetrized*
pullbacks of symmetric obstruction theories on moduli stacks\, using Kiem
-Savvas'étale-local notion of almost-perfect obstruction theory. I believ
e our techniques\, particularly the Joyce-style approach\, can also be app
lied to related questions such as DT/PT descendent transformations\, the D
T crepant resolution conjecture\, and the 4-fold DT/PT vertex corresponden
ce.\n
LOCATION:https://researchseminars.org/talk/M-seminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constantin Teleman (UC Berkeley)
DTSTART:20231005T203000Z
DTEND:20231005T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/107
DESCRIPTION:Title: Condensed Thoughts\nby Constantin Teleman (UC Berkeley) as part of
M-seminar\n\n\nAbstract\nTopological Field Theories have recently gained
attention via their control of (extended) topological operators in QFT. On
e operation commonly used in that context is ’condensation’\, which ho
wever seems to lack a precise definition. In this talk I will describe a p
ath to a precise construction of condensation and relate it to connectivit
y in the case of TQFTs coming from homotopy types. This is based on discus
sions with Dan Freed and Mike Hopkins\, in turn much inspired by conversat
ions with colleagues from the Simons Collaboration on Categorical Symmetri
es.\n
LOCATION:https://researchseminars.org/talk/M-seminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (MSU)
DTSTART:20231012T180000Z
DTEND:20231012T190000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/108
DESCRIPTION:Title: Cluster Nature of Quantum Groups\nby Linhui Shen (MSU) as part of
M-seminar\n\n\nAbstract\nWe present a rigid cluster model to realize the q
uantum group $U_q(g)$ for $g$ of type ADE. That is\, we prove that there i
s a natural Hopf algebra isomorphism from the quantum group to a quotient
algebra of the Weyl group invariants of a Fock-Goncharov quantum cluster a
lgebra. By applying the quantum duality of cluster algebras\, we show that
the quantum group admits a cluster canonical basis $\\Theta$ whose struct
ural coefficients are in $\\mathbb{N}[q^{\\frac{1}{2}}\, q^{-\\frac{1}{2}}
]$. The basis $\\Theta$ satisfies an invariance property under the braid g
roup action\, the Dynkin automorphisms\, and the star anti-involution. Bas
ed on the preprint arXiv: 2209.06258\n
LOCATION:https://researchseminars.org/talk/M-seminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niklas Garner (University of Washington)
DTSTART:20231017T203000Z
DTEND:20231017T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/109
DESCRIPTION:Title: Non-semisimple TQFTs from 3d N=4 QFTs - lecture 1\nby Niklas Garne
r (University of Washington) as part of M-seminar\n\n\nAbstract\nTopologic
al quantum field theory (TQFT) sits at the rich intersection of many disci
plines including physics\, topological\, and algebra. Many of the most fam
iliar TQFTs\, such as Chern-Simons theory with compact gauge group at posi
tive integer level\, can be built from semisimple categories where homolog
ical aspects can be safely avoided\, but this is no longer the case beyond
these simple examples. In these talks I will describe aspects of several
non-semisimple TQFTs arising from supersymmetric twists of three-dimension
al field theories and their relations to quantum groups and vertex operato
r algebras.\n
LOCATION:https://researchseminars.org/talk/M-seminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niklas Garner (University of Washington)
DTSTART:20231018T183000Z
DTEND:20231018T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/110
DESCRIPTION:Title: Non-semisimple TQFTs from 3d N=4 QFTs - lecture 2\nby Niklas Garne
r (University of Washington) as part of M-seminar\n\n\nAbstract\nTopologic
al quantum field theory (TQFT) sits at the rich intersection of many disci
plines including physics\, topological\, and algebra. Many of the most fam
iliar TQFTs\, such as Chern-Simons theory with compact gauge group at posi
tive integer level\, can be built from semisimple categories where homolog
ical aspects can be safely avoided\, but this is no longer the case beyond
these simple examples. In these talks I will describe aspects of several
non-semisimple TQFTs arising from supersymmetric twists of three-dimension
al field theories and their relations to quantum groups and vertex operato
r algebras.\n
LOCATION:https://researchseminars.org/talk/M-seminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niklas Garner (University of Washington)
DTSTART:20231019T203000Z
DTEND:20231019T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/111
DESCRIPTION:Title: Non-semisimple TQFTs from 3d N=4 QFTs - lecture 3\nby Niklas Garne
r (University of Washington) as part of M-seminar\n\n\nAbstract\nTopologic
al quantum field theory (TQFT) sits at the rich intersection of many disci
plines including physics\, topological\, and algebra. Many of the most fam
iliar TQFTs\, such as Chern-Simons theory with compact gauge group at posi
tive integer level\, can be built from semisimple categories where homolog
ical aspects can be safely avoided\, but this is no longer the case beyond
these simple examples. In these talks I will describe aspects of several
non-semisimple TQFTs arising from supersymmetric twists of three-dimension
al field theories and their relations to quantum groups and vertex operato
r algebras.\n
LOCATION:https://researchseminars.org/talk/M-seminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kapranov (IPMU)
DTSTART:20231108T200000Z
DTEND:20231108T210000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/112
DESCRIPTION:Title: Resurgent perverse sheaves\nby Mikhail Kapranov (IPMU) as part of
M-seminar\n\n\nAbstract\nPerverse sheaves provide a topological counterpar
t of regular holonomic D-modules whose solutions are multivalued functions
of certain restricted type. Much more general multivalued functions (on t
he complex plane C) have been studied in J. Ecalle's theory of resurgence
using\, as one of the main tools\, additive convolution. The talk\, based
on joint work in progress with Y. Soibelman\, will propose topological cou
nterpart of the theory of resurgence based on perverse sheaves on C which
are algebras with respect to (middle) additive convolution. Such sheaves t
ypically have infinitely many singular points. In particular\, we will arg
ue that the cohomological Hall algebra in a 3-Calabi-Yau situation localiz
es to such a "resurgent perverse sheaf".\n
LOCATION:https://researchseminars.org/talk/M-seminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Bryan (UBC)
DTSTART:20231026T203000Z
DTEND:20231026T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/113
DESCRIPTION:Title: The geometry and arithmetic of banana nano-manifolds\nby Jim Bryan
(UBC) as part of M-seminar\n\n\nAbstract\nThe Hodge numbers of a Calabi-Y
au threefold X are determined by the two numbers h^{1\,1}(X) and h^{1\,2}(
X) which can be interpreted respectively as the dimensions of the space of
Kahler forms and complex deformations respectively. We construct four new
examples X_N\, where N \\in {5\,6\,8\,9}\, of rigid Calabi-Yau threefolds
(h^{2\,1}=0) with Picard number 4 (h^{1\,1}=4). These manifolds are of
“banana type” and have among the smallest known values for Calabi-Yau
Hodge numbers. We (partially) compute the Donaldson-Thomas partition funct
ions of these manifolds and in particular show that the associated genus g
Gromov-Witten potential is given by a weight 2g-2 Siegel paramodular form
of index N. These manifolds are also modular in the arithmetic sense: the
re is a weight 4 modular form whose Fourier coefficients are obtained by c
ounting points over finite fields on X_N. We compute this form and observe
that it is the unique cusp form of weight 4 and index N. This is joint wo
rk with Stephen Pietromonaco.\n
LOCATION:https://researchseminars.org/talk/M-seminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Butson (Oxford University)
DTSTART:20231030T183000Z
DTEND:20231030T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/114
DESCRIPTION:Title: Vertex algebras from divisors on Calabi-Yau threefolds and perverse co
herent extensions - lecture 1\nby Dylan Butson (Oxford University) as
part of M-seminar\n\n\nAbstract\nWe will explain two conjecturally equival
ent constructions of vertex algebras associated to divisors S on certain t
oric Calabi-Yau threefolds Y\, and some partial results towards the proof
of their equivalence. One construction is algebraic\, as the kernel of scr
eening operators on lattice vertex algebras determined by the GKM graph of
Y and a Jordan-Holder filtration of the structure sheaf of S. The other i
s geometric\, as a convolution algebra acting on the homology of certain m
oduli spaces of sheaves supported on the divisor\, following the proof of
the AGT conjecture by Schiffmann-Vasserot and its generalization to diviso
rs in C^3 by Rapcak-Soibelman-Yang-Zhao. This provides a correspondence be
tween the enumerative geometry of sheaves on Calabi-Yau threefolds and the
representation theory of W-algebras and affine Yangian-type quantum group
s.\n
LOCATION:https://researchseminars.org/talk/M-seminar/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Butson (Oxford University)
DTSTART:20231101T183000Z
DTEND:20231101T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/115
DESCRIPTION:Title: Vertex algebras from divisors on Calabi-Yau threefolds and perverse co
herent extensions - lecture 2\nby Dylan Butson (Oxford University) as
part of M-seminar\n\n\nAbstract\nWe will explain two conjecturally equival
ent constructions of vertex algebras associated to divisors S on certain t
oric Calabi-Yau threefolds Y\, and some partial results towards the proof
of their equivalence. One construction is algebraic\, as the kernel of scr
eening operators on lattice vertex algebras determined by the GKM graph of
Y and a Jordan-Holder filtration of the structure sheaf of S. The other i
s geometric\, as a convolution algebra acting on the homology of certain m
oduli spaces of sheaves supported on the divisor\, following the proof of
the AGT conjecture by Schiffmann-Vasserot and its generalization to diviso
rs in C^3 by Rapcak-Soibelman-Yang-Zhao. This provides a correspondence be
tween the enumerative geometry of sheaves on Calabi-Yau threefolds and the
representation theory of W-algebras and affine Yangian-type quantum group
s.\n
LOCATION:https://researchseminars.org/talk/M-seminar/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Butson (Oxford University)
DTSTART:20231102T183000Z
DTEND:20231102T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/116
DESCRIPTION:Title: Vertex algebras from divisors on Calabi-Yau threefolds and perverse co
herent extensions - lecture 3\nby Dylan Butson (Oxford University) as
part of M-seminar\n\n\nAbstract\nWe will explain two conjecturally equival
ent constructions of vertex algebras associated to divisors S on certain t
oric Calabi-Yau threefolds Y\, and some partial results towards the proof
of their equivalence. One construction is algebraic\, as the kernel of scr
eening operators on lattice vertex algebras determined by the GKM graph of
Y and a Jordan-Holder filtration of the structure sheaf of S. The other i
s geometric\, as a convolution algebra acting on the homology of certain m
oduli spaces of sheaves supported on the divisor\, following the proof of
the AGT conjecture by Schiffmann-Vasserot and its generalization to diviso
rs in C^3 by Rapcak-Soibelman-Yang-Zhao. This provides a correspondence be
tween the enumerative geometry of sheaves on Calabi-Yau threefolds and the
representation theory of W-algebras and affine Yangian-type quantum group
s.\n
LOCATION:https://researchseminars.org/talk/M-seminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Butson (Oxford University)
DTSTART:20231103T183000Z
DTEND:20231103T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/117
DESCRIPTION:Title: Vertex algebras from divisors on Calabi-Yau threefolds and perverse co
herent extensions - lecture 4\nby Dylan Butson (Oxford University) as
part of M-seminar\n\n\nAbstract\nWe will explain two conjecturally equival
ent constructions of vertex algebras associated to divisors S on certain t
oric Calabi-Yau threefolds Y\, and some partial results towards the proof
of their equivalence. One construction is algebraic\, as the kernel of scr
eening operators on lattice vertex algebras determined by the GKM graph of
Y and a Jordan-Holder filtration of the structure sheaf of S. The other i
s geometric\, as a convolution algebra acting on the homology of certain m
oduli spaces of sheaves supported on the divisor\, following the proof of
the AGT conjecture by Schiffmann-Vasserot and its generalization to diviso
rs in C^3 by Rapcak-Soibelman-Yang-Zhao. This provides a correspondence be
tween the enumerative geometry of sheaves on Calabi-Yau threefolds and the
representation theory of W-algebras and affine Yangian-type quantum group
s.\n
LOCATION:https://researchseminars.org/talk/M-seminar/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harold Williams (USC)
DTSTART:20231116T213000Z
DTEND:20231116T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/118
DESCRIPTION:Title: Differential operators on the base affine space and quantized Coulomb
branches\nby Harold Williams (USC) as part of M-seminar\n\n\nAbstract\
nWe discuss joint work with Tom Gannon\, showing that the algebra $D(SL_n/
U)$ of differential operators on the base affine space of $SL_n$ is the qu
antized Coulomb branch of a certain 3d $\\mathcal{N} = 4$ quiver gauge the
ory. In the semiclassical limit this confirms a conjecture of Dancer-Hanan
y-Kirwan on the universal hyperk\\"ahler implosion of $SL_n$. In fact\, we
prove a generalization interpreting an arbitrary unipotent reduction of $
T^* SL_n$ as a Coulomb branch. These results also provide a new interpreta
tion of the Gelfand-Graev Weyl group symmetry of $D(SL_n/U)$.\n
LOCATION:https://researchseminars.org/talk/M-seminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Solomon (Hebrew University)
DTSTART:20231130T170000Z
DTEND:20231130T180000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/119
DESCRIPTION:Title: Counting holomorphic disks with boundary on the Chiang Lagrangian\
nby Jake Solomon (Hebrew University) as part of M-seminar\n\n\nAbstract\nI
will discuss a computation of open Gromov-Witten invariants counting holo
morphic disks with boundary on the Chiang Lagrangian along with various co
rrection terms. The Chiang Lagrangian is not fixed by an anti-symplectic i
nvolution and thus techniques from Floer theory are used instead of those
of real algebraic geometry that play a role in other computations. The inv
ariants exhibit periodic behaviors of periods 8 and 16. Denominators of in
variants are always powers of two indicating a non-trivial arithmetic stru
cture of the open WDVV equations. Background on open Gromov-Witten theory
will be provided. This is joint work with Hollands-Kosloff-Sela-Shu and Tu
kachinsky.\n
LOCATION:https://researchseminars.org/talk/M-seminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Pardon (Simons Center)
DTSTART:20231206T183000Z
DTEND:20231206T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/120
DESCRIPTION:Title: Universally counting curves in Calabi--Yau threefolds\nby John Par
don (Simons Center) as part of M-seminar\n\n\nAbstract\nEnumerating curves
in algebraic varieties traditionally involves choosing a compactification
of the space of smooth embedded curves in the variety. There are many suc
h compactifications\, hence many different enumerative invariants. I will
propose a "universal" (very tautological) enumerative invariant which take
s values in a certain Grothendieck group of 1-cycles. It is often the case
with such "universal" constructions that the resulting Grothendieck group
is essentially uncomputable. But in this case\, the cluster formalism of
Ionel and Parker shows that\, in the case of threefolds with nef anticanon
ical bundle\, this Grothendieck group is freely generated by local curves.
This reduces the MNOP conjecture (in the case of nef anticanonical bundle
and primary insertions) to the case of local curves\, where it is already
known due to work of Bryan--Pandharipande and Okounkov--Pandharipande.\n
LOCATION:https://researchseminars.org/talk/M-seminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Edinburgh)
DTSTART:20240208T200000Z
DTEND:20240208T210000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/121
DESCRIPTION:Title: Perverse sheaves in deformation quantization\nby Pavel Safronov (U
niversity of Edinburgh) as part of M-seminar\n\n\nAbstract\nGiven a holomo
rphic symplectic manifold\, there is a canonical category of deformation q
uantization modules. Holomorphic Lagrangians equipped with spin structures
define objects in this category. I will explain how one can describe the
RHom perverse sheaf of two such DQ modules in terms of the derived geometr
y of the Lagrangian intersection. I will also explain a related result des
cribing the perverse sheaf appearing in BV quantization of a (-1)-shifted
symplectic scheme. This is a report on work joint with Sam Gunningham.\n
LOCATION:https://researchseminars.org/talk/M-seminar/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (University of Edinburgh)
DTSTART:20240219T193000Z
DTEND:20240219T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/122
DESCRIPTION:Title: Cohomological Hall algebras of 2-Calabi-Yau categories and application
s (lecture 1)\nby Lucien Hennecart (University of Edinburgh) as part o
f M-seminar\n\n\nAbstract\nIn this series of four lectures\, I will explai
n the interactions between cohomological Hall algebras (CoHAs) and several
questions of interest in algebraic geometry (in particular enumerative ge
ometry) and representation theory (Kac-Moody algebras and their representa
tions).\n\nCoHAs are associative algebra structures on the Borel-Moore hom
ology of the stack of objects in some Abelian categories. We consider the
CoHAs of various categories: sheaves on surfaces\, representations of quiv
ers\, and representations of fundamental groups\, which are 2-Calabi-Yau.
CoHAs lead to a fine understanding of the cohomology of the stacks and mod
uli spaces involved. They provide tools to study various conjectures in th
e subject: cohomological integrality\, positivity\, and purity. In the fir
st two lectures\, I will detail how CoHAs give a geometric construction of
generalised Kac-Moody algebras (in the sense of Borcherds). The last two
lectures will develop applications of CoHAs to the study of the cohomology
of quiver varieties (following the groundbreaking work of Nakajima from t
he 1990s) and to nonabelian Hodge theory (following questions of Simpson).
\n\nThe four lectures will\, to a large extent\, be independent from each
other and are largely based on joint work with Ben Davison and Sebastian S
chlegel Mejia.\n
LOCATION:https://researchseminars.org/talk/M-seminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (University of Edinburgh)
DTSTART:20240221T193000Z
DTEND:20240221T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/123
DESCRIPTION:Title: Cohomological Hall algebras of 2-Calabi-Yau categories and application
s (lecture 2)\nby Lucien Hennecart (University of Edinburgh) as part o
f M-seminar\n\n\nAbstract\nIn this series of four lectures\, I will explai
n the interactions between cohomological Hall algebras (CoHAs) and several
questions of interest in algebraic geometry (in particular enumerative ge
ometry) and representation theory (Kac-Moody algebras and their representa
tions).\n\nCoHAs are associative algebra structures on the Borel-Moore hom
ology of the stack of objects in some Abelian categories. We consider the
CoHAs of various categories: sheaves on surfaces\, representations of quiv
ers\, and representations of fundamental groups\, which are 2-Calabi-Yau.
CoHAs lead to a fine understanding of the cohomology of the stacks and mod
uli spaces involved. They provide tools to study various conjectures in th
e subject: cohomological integrality\, positivity\, and purity. In the fir
st two lectures\, I will detail how CoHAs give a geometric construction of
generalised Kac-Moody algebras (in the sense of Borcherds). The last two
lectures will develop applications of CoHAs to the study of the cohomology
of quiver varieties (following the groundbreaking work of Nakajima from t
he 1990s) and to nonabelian Hodge theory (following questions of Simpson).
\n\nThe four lectures will\, to a large extent\, be independent from each
other and are largely based on joint work with Ben Davison and Sebastian S
chlegel Mejia.\n
LOCATION:https://researchseminars.org/talk/M-seminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (University of Edinburgh)
DTSTART:20240222T213000Z
DTEND:20240222T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/124
DESCRIPTION:Title: Cohomological Hall algebras of 2-Calabi-Yau categories and application
s (lecture 3)\nby Lucien Hennecart (University of Edinburgh) as part o
f M-seminar\n\n\nAbstract\nIn this series of four lectures\, I will explai
n the interactions between cohomological Hall algebras (CoHAs) and several
questions of interest in algebraic geometry (in particular enumerative ge
ometry) and representation theory (Kac-Moody algebras and their representa
tions).\n\nCoHAs are associative algebra structures on the Borel-Moore hom
ology of the stack of objects in some Abelian categories. We consider the
CoHAs of various categories: sheaves on surfaces\, representations of quiv
ers\, and representations of fundamental groups\, which are 2-Calabi-Yau.
CoHAs lead to a fine understanding of the cohomology of the stacks and mod
uli spaces involved. They provide tools to study various conjectures in th
e subject: cohomological integrality\, positivity\, and purity. In the fir
st two lectures\, I will detail how CoHAs give a geometric construction of
generalised Kac-Moody algebras (in the sense of Borcherds). The last two
lectures will develop applications of CoHAs to the study of the cohomology
of quiver varieties (following the groundbreaking work of Nakajima from t
he 1990s) and to nonabelian Hodge theory (following questions of Simpson).
\n\nThe four lectures will\, to a large extent\, be independent from each
other and are largely based on joint work with Ben Davison and Sebastian S
chlegel Mejia.\n
LOCATION:https://researchseminars.org/talk/M-seminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (University of Edinburgh)
DTSTART:20240223T193000Z
DTEND:20240223T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/125
DESCRIPTION:Title: Cohomological Hall algebras of 2-Calabi-Yau categories and application
s (lecture 4)\nby Lucien Hennecart (University of Edinburgh) as part o
f M-seminar\n\n\nAbstract\nIn this series of four lectures\, I will explai
n the interactions between cohomological Hall algebras (CoHAs) and several
questions of interest in algebraic geometry (in particular enumerative ge
ometry) and representation theory (Kac-Moody algebras and their representa
tions).\n\nCoHAs are associative algebra structures on the Borel-Moore hom
ology of the stack of objects in some Abelian categories. We consider the
CoHAs of various categories: sheaves on surfaces\, representations of quiv
ers\, and representations of fundamental groups\, which are 2-Calabi-Yau.
CoHAs lead to a fine understanding of the cohomology of the stacks and mod
uli spaces involved. They provide tools to study various conjectures in th
e subject: cohomological integrality\, positivity\, and purity. In the fir
st two lectures\, I will detail how CoHAs give a geometric construction of
generalised Kac-Moody algebras (in the sense of Borcherds). The last two
lectures will develop applications of CoHAs to the study of the cohomology
of quiver varieties (following the groundbreaking work of Nakajima from t
he 1990s) and to nonabelian Hodge theory (following questions of Simpson).
\n\nThe four lectures will\, to a large extent\, be independent from each
other and are largely based on joint work with Ben Davison and Sebastian S
chlegel Mejia.\n
LOCATION:https://researchseminars.org/talk/M-seminar/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gus Schrader (Northwestern University)
DTSTART:20240215T190000Z
DTEND:20240215T200000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/126
DESCRIPTION:Title: Skeins\, clusters and wavefunctions\nby Gus Schrader (Northwestern
University) as part of M-seminar\n\n\nAbstract\nEkholm and Shende have pr
oposed a version of open Gromov-Witten theory in which holomorphic maps fr
om Riemann surfaces with boundary landing on a Lagrangian 3-manifold L are
counted via the image of the boundary in the HOMFLYPT skein module of L.
I'll describe joint work with Mingyuan Hu and Eric Zaslow which gives a me
thod to compute the Ekholm-Shende generating function ('wavefunction') enu
merating such maps for a class of Lagrangian branes L in C^3. The method u
ses a skein-theoretic analog of cluster theory\, in which skein-valued wav
efunctions for different Lagrangians are related by skein mutation operato
rs.\n
LOCATION:https://researchseminars.org/talk/M-seminar/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20240227T213000Z
DTEND:20240227T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/127
DESCRIPTION:Title: Periodic pencils of flat connections and their p-curvature\nby Pav
el Etingof (MIT) as part of M-seminar\n\n\nAbstract\nA periodic pencil of
flat connections on a smooth algebraic variety $X$ is a linear family of f
lat connections $\\nabla(s_1\,...\,s_n)=d-\\sum_{i=1}^r\\sum_{j=1}^ns_jB_{
ij}dx_i$\, where $\\lbrace x_i\\rbrace$ are local coordinates on $X$ and $
B_{ij}: X\\to {\\rm Mat}_N$ are matrix-valued regular functions. A pencil
is periodic if it is generically invariant under the shifts $s_j\\mapsto s
_j+1$ up to isomorphism. I will explain that periodic pencils have many re
markable properties\, and there are many interesting examples of them\, e.
g. Knizhnik-Zamolodchikov\, Dunkl\, Casimir connections and equivariant qu
antum connections for conical symplectic resolutions with finitely many to
rus fixed points. I will also explain that in characteristic $p$\, the $p$
-curvature operators $\\lbrace C_i\,1\\le i\\le r\\rbrace$ of a periodic p
encil $\\nabla$ are isospectral to the commuting endomorphisms $C_i^*:=\\s
um_{j=1}^n (s_j-s_j^p)B_{ij}^{(1)}$\, where $B_{ij}^{(1)}$ is the Frobeniu
s twist of $B_{ij}$. This allows us to compute the eigenvalues of the $p$-
curvature for the above examples\, and also to show that a periodic pencil
of connections always has regular singularites. This is joint work with A
lexander Varchenko.\n
LOCATION:https://researchseminars.org/talk/M-seminar/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Minets (MPI Bonn)
DTSTART:20240307T213000Z
DTEND:20240307T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/128
DESCRIPTION:Title: COHAs of 0-dimensional sheaves on surfaces\nby Alexandre Minets (M
PI Bonn) as part of M-seminar\n\n\nAbstract\nGiven an abelian category C o
f low homological dimension\, one can construct a cohomological Hall algeb
ra (COHA) of C\, whose product encodes extensions between objects in C. An
important example of such C is the category Coh(S) of coherent sheaves on
a smooth surface S. While understanding the whole CoHA algebraically is m
ore or less hopeless for a general S\, we can restrict our attention to th
e CoHA of 0-dimensional sheaves. I will give an explicit description of th
is algebra\, which builds on the seminal work of Nakajima and Lehn. I will
also discuss how this description can be used to deduce structural result
s about cohomology of moduli spaces of sheaves with positive-dimensional s
upport on S\, such as our recent proof of P=W conjecture. This is a report
on joint work with A. Mellit\, O. Schiffmann and E. Vasserot.\n
LOCATION:https://researchseminars.org/talk/M-seminar/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Botta (ETH)
DTSTART:20240321T193000Z
DTEND:20240321T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/129
DESCRIPTION:Title: Maulik-Okounkov Lie algebras and BPS Lie algebras\nby Tommaso Bott
a (ETH) as part of M-seminar\n\n\nAbstract\nThe Maulik-Okounkov (MO) Lie a
lgebra associated to a quiver Q controls the R-matrix formalism developed
by Maulik and Okounkov in the context of (quantum) cohomology of Nakajima
quiver varieties. On the other hand\, the BPS Lie algebra originates from
cohomological DT theory\, and in particular from the theory of cohomologic
al Hall algebras associated to 3 Calabi-Yau categories. In this talk\, I w
ill explain how to identify the MO Lie algebra of Q with the BPS Lie algeb
ra of the tripled quiver Q̃ with its canonical cubic potential. The bridg
e to compare these similarly diverse words is the theory of non-abelian st
able envelopes\, which can be exploited to relate representations of the M
O Lie algebra to representations of the BPS Lie algebra. As a byproduct\,
I will present a proof of Okounkov's conjecture\, equating the graded dime
nsions of the MO Lie algebra with the coefficients of Kac polynomials. Thi
s is joint work with Ben Davison.\n
LOCATION:https://researchseminars.org/talk/M-seminar/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwei Yun (MIT)
DTSTART:20240328T203000Z
DTEND:20240328T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/130
DESCRIPTION:Title: An irregular Deligne-Simpson problem\nby Zhiwei Yun (MIT) as part
of M-seminar\n\n\nAbstract\nThe Deligne-Simpson problem asks for a criteri
on for the existence of connections on an algebraic curve with prescribed
singularities at punctures. We give a solution to a generalization of this
problem to G-connections on P^1 with a regular singularity and an irregul
ar singularity (satisfying a condition called isoclinic). Here G can be an
y complex reductive group. Perhaps surprisingly\, the solution can be expr
essed in terms of rational Cherednik algebras. This is joint work with Kon
stantin Jakob\, and the proof uses recent joint work with Bezrukavnikov\,
Boixeda Alvarez and McBreen\, and previous joint work with Oblomkov.\n
LOCATION:https://researchseminars.org/talk/M-seminar/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nekrasov (Simons Center)
DTSTART:20240404T203000Z
DTEND:20240404T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/131
DESCRIPTION:Title: Infinite-dimensional spin chains from gauge theory\nby Nikita Nekr
asov (Simons Center) as part of M-seminar\n\n\nAbstract\nSpin chains are q
uantum mechanical models of interacting degrees of freedom\, such as (anti
)ferromagnetic atoms. The celebrated Bethe ansatz for the eigenstates of t
he Heisenberg spin chain Hamiltonian has been a source of inspiration for
physicists and mathematicians for almost a century now\, leading to the in
vention of quantum groups\, among other achievements. In my talk I will de
scribe several infinite-dimensional generalizations of spin chains\, which
are believed to play an important role in the studies of strong interacti
ons of elementary particles: L.Lipatov's reggeized gluons\, planar N=4 sup
er-Yang-Mills anomalous dimensions and\, closer to the seminar's theme: su
rface defects in N=2 super-QCD. Mathematically\, the latter is the generat
ing function of equivariant DT-type invariants defined via the moduli spac
es of parabolic sheaves on complex surfaces. Surprisingly\, the Hecke oper
ators of geometric and analytic Langlands programs make appearances\, and
gauge theory allows them to generalize outside the critical level. Based o
n the recent work with Saebyeok Jeong\, Norton Lee\, and on the recent wor
k and work in progress with Andrey Grekov\n
LOCATION:https://researchseminars.org/talk/M-seminar/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20240408T183000Z
DTEND:20240408T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/132
DESCRIPTION:Title: Dispatches from the ends of the stability manifold - part 1\nby Da
niel Halpern-Leistner (Cornell University) as part of M-seminar\n\n\nAbstr
act\nThis is the first lecture of four.\n\nThe manifold of Bridgeland stab
ility conditions parameterizes a homological structure on a triangulated c
ategory that is analogous to a Kaehler structure on a projective variety.
Recently\, I have proposed a "noncommutative minimal model program" in whi
ch the quantum differential equation of a projective variety determines pa
ths toward infinity in the stability manifold of that variety\, and that t
hese paths can be used to define canonical (semiorthogonal)decompositions
of its derived category.\nIn fact\, these paths converge in a certain part
ial compactification of the stability manifold\, the space of "augmented s
tability conditions." In order to define this partial compactification\, I
will introduce a structure on a triangulated category that we call a mult
i-scale decomposition\, which generalizes a semiorthogonal decomposition\,
and a new moduli space of multi-scale lines that is closely related to th
e moduli spaces of multi-scale differentials which are of recent interest
in dynamics. The main conjecture about the space of augmented stability co
nditions is that it is a manifold with corners (in a specific way that I w
ill explain). One consequence: If this conjecture holds for any smooth and
proper dg-category\, then any stability condition on a smooth and proper
dg-category admits proper moduli spaces of semistable objects.\nThe plan f
or the lectures is\, loosely:\n1) The noncommutative MMP\n2) The space of
n-pointed multi-scale lines (lecture on Wednesday will be given by Alekos
Robotis)\n3) The space of augmented stability conditions\n4) Structure of
the boundary: the manifold-with-corners conjecture and consequences\n
LOCATION:https://researchseminars.org/talk/M-seminar/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20240410T183000Z
DTEND:20240410T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/133
DESCRIPTION:Title: Dispatches from the ends of the stability manifold - part 2\nby Da
niel Halpern-Leistner (Cornell University) as part of M-seminar\n\n\nAbstr
act\nThis is the second lecture of four.\n\nThe manifold of Bridgeland sta
bility conditions parameterizes a homological structure on a triangulated
category that is analogous to a Kaehler structure on a projective variety.
Recently\, I have proposed a "noncommutative minimal model program" in wh
ich the quantum differential equation of a projective variety determines p
aths toward infinity in the stability manifold of that variety\, and that
these paths can be used to define canonical (semiorthogonal)decompositions
of its derived category.\nIn fact\, these paths converge in a certain par
tial compactification of the stability manifold\, the space of "augmented
stability conditions." In order to define this partial compactification\,
I will introduce a structure on a triangulated category that we call a mul
ti-scale decomposition\, which generalizes a semiorthogonal decomposition\
, and a new moduli space of multi-scale lines that is closely related to t
he moduli spaces of multi-scale differentials which are of recent interest
in dynamics. The main conjecture about the space of augmented stability c
onditions is that it is a manifold with corners (in a specific way that I
will explain). One consequence: If this conjecture holds for any smooth an
d proper dg-category\, then any stability condition on a smooth and proper
dg-category admits proper moduli spaces of semistable objects.\nThe plan
for the lectures is\, loosely:\n1) The noncommutative MMP\n2) The space of
n-pointed multi-scale lines (lecture on Wednesday will be given by Alekos
Robotis)\n3) The space of augmented stability conditions\n4) Structure of
the boundary: the manifold-with-corners conjecture and consequences\n
LOCATION:https://researchseminars.org/talk/M-seminar/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20240411T203000Z
DTEND:20240411T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/134
DESCRIPTION:Title: Dispatches from the ends of the stability manifold - part 3\nby Da
niel Halpern-Leistner (Cornell University) as part of M-seminar\n\n\nAbstr
act\nThis is the third lecture of four.\n\nThe manifold of Bridgeland stab
ility conditions parameterizes a homological structure on a triangulated c
ategory that is analogous to a Kaehler structure on a projective variety.
Recently\, I have proposed a "noncommutative minimal model program" in whi
ch the quantum differential equation of a projective variety determines pa
ths toward infinity in the stability manifold of that variety\, and that t
hese paths can be used to define canonical (semiorthogonal)decompositions
of its derived category.\nIn fact\, these paths converge in a certain part
ial compactification of the stability manifold\, the space of "augmented s
tability conditions." In order to define this partial compactification\, I
will introduce a structure on a triangulated category that we call a mult
i-scale decomposition\, which generalizes a semiorthogonal decomposition\,
and a new moduli space of multi-scale lines that is closely related to th
e moduli spaces of multi-scale differentials which are of recent interest
in dynamics. The main conjecture about the space of augmented stability co
nditions is that it is a manifold with corners (in a specific way that I w
ill explain). One consequence: If this conjecture holds for any smooth and
proper dg-category\, then any stability condition on a smooth and proper
dg-category admits proper moduli spaces of semistable objects.\nThe plan f
or the lectures is\, loosely:\n1) The noncommutative MMP\n2) The space of
n-pointed multi-scale lines (lecture on Wednesday will be given by Alekos
Robotis)\n3) The space of augmented stability conditions\n4) Structure of
the boundary: the manifold-with-corners conjecture and consequences\n
LOCATION:https://researchseminars.org/talk/M-seminar/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20240412T183000Z
DTEND:20240412T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/135
DESCRIPTION:Title: Dispatches from the ends of the stability manifold - part 4\nby Da
niel Halpern-Leistner (Cornell University) as part of M-seminar\n\n\nAbstr
act\nThis is the fourth lecture of four.\n\nThe manifold of Bridgeland sta
bility conditions parameterizes a homological structure on a triangulated
category that is analogous to a Kaehler structure on a projective variety.
Recently\, I have proposed a "noncommutative minimal model program" in wh
ich the quantum differential equation of a projective variety determines p
aths toward infinity in the stability manifold of that variety\, and that
these paths can be used to define canonical (semiorthogonal)decompositions
of its derived category.\nIn fact\, these paths converge in a certain par
tial compactification of the stability manifold\, the space of "augmented
stability conditions." In order to define this partial compactification\,
I will introduce a structure on a triangulated category that we call a mul
ti-scale decomposition\, which generalizes a semiorthogonal decomposition\
, and a new moduli space of multi-scale lines that is closely related to t
he moduli spaces of multi-scale differentials which are of recent interest
in dynamics. The main conjecture about the space of augmented stability c
onditions is that it is a manifold with corners (in a specific way that I
will explain). One consequence: If this conjecture holds for any smooth an
d proper dg-category\, then any stability condition on a smooth and proper
dg-category admits proper moduli spaces of semistable objects.\nThe plan
for the lectures is\, loosely:\n1) The noncommutative MMP\n2) The space of
n-pointed multi-scale lines (lecture on Wednesday will be given by Alekos
Robotis)\n3) The space of augmented stability conditions\n4) Structure of
the boundary: the manifold-with-corners conjecture and consequences\n
LOCATION:https://researchseminars.org/talk/M-seminar/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroshi Iritani (Kyoto University)
DTSTART:20240418T140000Z
DTEND:20240418T150000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/136
DESCRIPTION:Title: Decomposition of quantum cohomology under blowups\nby Hiroshi Irit
ani (Kyoto University) as part of M-seminar\n\n\nAbstract\nQuantum cohomol
ogy is a deformation of the cohomology ring defined by counting rational c
urves. A close relationship between quantum cohomology and birational geom
etry has been expected. For example\, when the quantum parameter q approac
hes an "extremal ray"\, the spectrum of the quantum cohomology ring cluste
rs in a certain way (predicted by the corresponding extremal contraction)\
, inducing a decomposition of the quantum cohomology. In this talk\, I wil
l discuss such a decomposition for blowups: quantum cohomology of the blow
up of X along a smooth center Z will decompose into QH(X) and (codim Z-1)
copies of QH(Z). The proof relies on Fourier analysis and shift operators
for equivariant quantum cohomology. We can describe blowups as a variation
of GIT of a certain space W with C^* action. The equivariant quantum coho
mology of W acts as a "global" mirror family connecting X and its blowup.\
n
LOCATION:https://researchseminars.org/talk/M-seminar/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murad Alim (Heriot-Watt University)
DTSTART:20240425T203000Z
DTEND:20240425T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/137
DESCRIPTION:Title: From Gromov-Witten to Donaldson-Thomas invariants via resurgence\n
by Murad Alim (Heriot-Watt University) as part of M-seminar\n\n\nAbstract\
nThe generating function of higher genus Gromov-Witten invariants of Calab
i-Yau threefolds can be computed by topological string theory and is given
by an asymptotic series in the topological string coupling. I will discus
s how a piecewise analytic function in the string coupling can be obtained
from this series via resurgence analysis and how Donaldson-Thomas invaria
nts of the same geometry can be obtained from the corresponding Stokes fac
tors. This is based on various joint works with Lotte Hollands\, Arpan Sah
a\, Iván Tulli and Jörg Teschner as well as on work in progress.\n
LOCATION:https://researchseminars.org/talk/M-seminar/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheel Ganatra (USC)
DTSTART:20240502T180000Z
DTEND:20240502T190000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/138
DESCRIPTION:Title: Arclike Lagrangians in Liouville sectors\nby Sheel Ganatra (USC) a
s part of M-seminar\n\n\nAbstract\nSectorial descent\, established in earl
ier joint work with Pardon-Shende\, gives a local-to-global formula comput
ing the wrapped Fukaya category of a Weinstein manifold from a sectorial c
over. If one has a specific fixed global Lagrangian in mind that isn't con
tained in a single subsector\, the resulting formula is only implicit\, as
it begins by appealing to the generation of this object by "local" Lagran
gians. In this talk I will introduce and study the class of (global) "arcl
ike" Lagrangian submanifolds with respect to a sectorial covering\, which
are allowed to run through subsector boundaries but in a controlled fashio
n. For arclike Lagrangians\, a more explicit local-to-global analysis is p
ossible. Based on works in progress with Hanlon-Hicks-Pomerleano-Sheridan
and Hanlon-Hicks-Ward.\n
LOCATION:https://researchseminars.org/talk/M-seminar/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gwyn Bellamy (University of Glasgow)
DTSTART:20240905T150000Z
DTEND:20240905T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/139
DESCRIPTION:Title: Koszul Duality on quantizations of bionic symplectic varieties\nby
Gwyn Bellamy (University of Glasgow) as part of M-seminar\n\n\nAbstract\n
Via localization theorems à la Beilinson-Bernstein\, representations of q
uantizations of symplectic singularities are equivalent to modules over sh
eaves of deformation-quantization algebras (DQ-modules) on symplectic reso
lutions of the singularity. This applies for instance to (spherical) ratio
nal Cherednik algebras and finite W-algebras as well as the primitive cent
ral quotients of enveloping algebras appearing in the original Beilinson-B
ernstein theorem. Usually\, the sympletic resolution is equipped with a Ha
miltonian C*-action\, who attracting locus is a Lagrangian (with modules s
upported on this Lagrangian belonging to geometric category O). I'll expla
in that it's possible to construct a "local generator" in geometric catego
ry O such that the bounded derived category of coherent DQ-modules is equi
valent to the derived category of coherent modules over the dg-endomorphis
m ring of the generator. This is a generalization of the classical D-Omega
duality of Kapranov\, Beilinson-Drinfeld and Positselski and thus an exam
ple of filtered Koszul duality. This talk is based on recent joint work wi
th Chris Dodd\, Kevin McGerty and Tom Nevins.\n
LOCATION:https://researchseminars.org/talk/M-seminar/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingyuan Hu (Northwestern University)
DTSTART:20240912T193000Z
DTEND:20240912T203000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/140
DESCRIPTION:Title: Skein valued open Gromov-Witten invariants and cluster mutations\n
by Mingyuan Hu (Northwestern University) as part of M-seminar\n\n\nAbstrac
t\nWe consider a class of Lagrangians living in [\\mathbb{C}^3] . Their Ek
holm-Shende wavefunctions\, living in the HOMFLY-PT skein module\, will en
code open Gromov-Witten invariants in all genus and with arbitrary numbers
of boundary components. We develop a skein valued cluster theory to compu
te these wavefunctions. In the case of Aganagic-Vafa brane\, our computati
on matches up with the prediction of the topological vertex. We also defin
e a skein-valued dilogarithm and prove a relation. which will imply the 5-
term relation of Garsia and Mellit. This talk is based on arXiv:2312.10186
(joint with Gus Schrader and Eric Zaslow) and arXiv:2401.10817.\n
LOCATION:https://researchseminars.org/talk/M-seminar/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hulya Arguz (U Georgia)
DTSTART:20240926T203000Z
DTEND:20240926T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/141
DESCRIPTION:Title: The KSBA moduli space of stable log Calabi-Yau surfaces\nby Hulya
Arguz (U Georgia) as part of M-seminar\n\n\nAbstract\nThe KSBA moduli spac
e\, introduced by Kollár--Shepherd-Barron\, and Alexeev\, is a natural ge
neralization of "the moduli space of stable curves" to higher dimensions.
It parametrizes stable pairs (X\,B)\, where X is a projective algebraic va
riety satisfying certain conditions and B is a divisor such that K_X+B is
ample. This moduli space is described concretely only in a handful of situ
ations: for instance\, if X is a toric variety and B=D+\\epsilon C\, where
D is the toric boundary divisor and C is an ample divisor\, it is shown b
y Alexeev that the KSBA moduli space is a toric variety. Generally\, for a
log Calabi-Yau variety (X\,D) consisting of a projective variety X and an
anticanonical divisor D\, with B=D+\\epsilon C where C is an ample diviso
r\, it was conjectured by Hacking--Keel--Yu that the KSBA moduli space is
still toric (up to passing to a finite cover). In joint work with Alexeev
and Bousseau\, we prove this conjecture for all log Calabi-Yau surfaces. T
his uses tools from the minimal model program\, log smooth deformation the
ory and mirror symmetry.\n
LOCATION:https://researchseminars.org/talk/M-seminar/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hicks (University of Edinburgh)
DTSTART:20241003T203000Z
DTEND:20241003T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/142
DESCRIPTION:Title: Superabundance and Unobstructedness\nby Jeff Hicks (University of
Edinburgh) as part of M-seminar\n\n\nAbstract\nConsider a tropical curve i
n the base of a Lagrangian torus fibration. Then there exists a "Lagrangia
n realization" of this curve: a Lagrangian submanifold in the total space
of the fibration whose projection to the base can be made to lie (via Hami
ltonian isotopy) arbitrarily close to your original tropical curve. In thi
s talk\, we'll show that in the 3-dimensional setting a combinatorial crit
erion (non-superabundance of the tropical curve) determines unobstructedne
ss of the corresponding Lagrangian lift.\n
LOCATION:https://researchseminars.org/talk/M-seminar/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shivang Jingdal (University of Edinburgh)
DTSTART:20241010T150000Z
DTEND:20241010T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/143
DESCRIPTION:Title: CoHA of cyclic quivers and an integral form of affine Yangians\nby
Shivang Jingdal (University of Edinburgh) as part of M-seminar\n\n\nAbstr
act\nIn 2012\, Schiffmann and Vasserot considered a Hall algebra-type cons
truction on the cohomology of the moduli space of sheaves supported on poi
nts in a plane\, using it to prove the AGT conjecture. However\, due to th
e mysterious nature of the moduli space of representations of the preproje
ctive algebra\, these algebras are very difficult to study and are often h
ighly nontrivial. In this talk\, my goal is to explain how one can study t
his algebra by employing tools from cohomological Donaldson-Thomas theory.
In particular\, I will explain how\, in the case of the cyclic quiver\, t
his algebra turns out to be the universal enveloping algebra of the positi
ve half of a certain extension of matrix differential operators on the tor
us\, while its deformation turns out to be an explicit integral form of th
e affine Yangian of gl(n).\n
LOCATION:https://researchseminars.org/talk/M-seminar/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Mclean (Stony Brook)
DTSTART:20241017T203000Z
DTEND:20241017T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/144
DESCRIPTION:Title: Symplectic Orbifold Gromov-Witten Invariants\nby Mark Mclean (Ston
y Brook) as part of M-seminar\n\n\nAbstract\nChen and Ruan constructed sym
plectic orbifold Gromov-Witten invariants more than 20 years ago. In ongoi
ng work with Alex Ritter\, we show that moduli spaces of pseudo-holomorphi
c curves mapping to a symplectic orbifold admit global Kuranishi charts. T
his allows us to construct other types of Gromov-Witten invariants\, such
as K-theoretic counts. The construction relies on an orbifold embedding th
eorem of Ross and Thomas.\n
LOCATION:https://researchseminars.org/talk/M-seminar/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Hoskins (Radboud University)
DTSTART:20241024T150000Z
DTEND:20241024T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/145
DESCRIPTION:Title: Moduli spaces of bundles on curves with abelian motives\nby Victor
ia Hoskins (Radboud University) as part of M-seminar\n\n\nAbstract\nI will
explain how several different moduli spaces of bundles on a curve have ab
elian motives and how conservatively properties for abelian motives can be
harnessed to obtain motivic formulas and provide motivic lifts of known c
ohomological phenomena\, such as chi-independence and mirror symmetry. Thi
s is joint work with Simon Pepin Lehalleur.\n
LOCATION:https://researchseminars.org/talk/M-seminar/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zihong Chen (MIT)
DTSTART:20241031T203000Z
DTEND:20241031T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/146
DESCRIPTION:Title: The exponential type conjecture for quantum connections\nby Zihong
Chen (MIT) as part of M-seminar\n\n\nAbstract\nThe (small) quantum connec
tion is one of the simplest objects built out of Gromov-Witten theory\, ye
t it gives rise to a repertoire of rich and important questions such as th
e Gamma conjectures and the Dubrovin conjectures. There is a very basic qu
estion one can ask about this connection: what is its formal singularity t
ype? People's (e.g. Kontsevich-Katzarkov-Pantev\, Iritani) expectation for
this is packaged into the so-called exponential type conjecture\, and the
goal of this talk is to discuss a proof in the case of closed monotone sy
mplectic manifolds. My approach uses a reduction mod p argument\, and I wi
ll start by introducing some basic ordinary differential equations (in par
ticular in characteristic p) and Katz's local monodromy theorem. Then I wi
ll demonstrate the key idea of proof pretending we were working in a B-sid
e mirror situation---matrix factorizations\, where it is particularly simp
le. Finally\, I will explain how to adapt the proof to the case of quantum
connections using certain equivariant operations on quantum cohomology.\n
LOCATION:https://researchseminars.org/talk/M-seminar/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sala (University of Pisa)
DTSTART:20241107T160000Z
DTEND:20241107T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/147
DESCRIPTION:Title: Cohomological Hall algebras\, their representations\, and Nakajima ope
rators\nby Francesco Sala (University of Pisa) as part of M-seminar\n\
n\nAbstract\nIn the first part of the talk\, I will briefly introduce the
theory of 2d cohomological Hall algebras (COHAs)\, focusing on the example
of COHAs arising from zero-dimensional sheaves on smooth surfaces. I will
also describe certain geometric representations of these COHAs and introd
uce Nakajima-type operators. In the second part\, I will discuss a general
ization and categorification of this framework.\n
LOCATION:https://researchseminars.org/talk/M-seminar/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Tessler (Weizmann Institute of Science)
DTSTART:20241114T190000Z
DTEND:20241114T200000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/148
DESCRIPTION:Title: Open Mirror Symmetry for Landau-Ginzburg Models\nby Ran Tessler (W
eizmann Institute of Science) as part of M-seminar\n\n\nAbstract\nWe will
start with a short overview of mirror symmetry. We will then describe Sait
o-Givental's theory and its mirror dual using FJRW theory and open FJRW th
eory. Based on joint works with Mark Gross and Tyler Kelly.\n
LOCATION:https://researchseminars.org/talk/M-seminar/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Grekov (Simons Center)
DTSTART:20241121T160000Z
DTEND:20241121T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/149
DESCRIPTION:Title: Many-body integrable systems and the moduli space of instantons: Quant
um spectral curves and classical Lax operators\nby Andrei Grekov (Simo
ns Center) as part of M-seminar\n\n\nAbstract\nIn this talk\, I will explo
re the relation between the generalized equivariant cohomology theories of
the moduli space of instantons on \\mathbb{C}^2 and the famous family of
integrable systems: Calogero-Moser\, Ruijsennars-Schneider\, and DELL. We
introduce the so-called \\theta-transforms of the qq-characters vev’s\,
defined as integrals of certain classes in these cohomology theories\, and
relate them to quantum spectral curves of the corresponding integrable sy
stems. The solution to the quantum spectral curve equation is constructed
in a natural way as well. In the second half\, I will explain the orbifold
ed version of all the notions defined above\, which corresponds to the rep
lacement of the moduli space of instantons with the affine Laumon space. S
uch treatment allows one to obtain the Lax matrices of the integrable syst
ems in question in a new form\, as well as the eigenvectors of these matri
ces. In the end\, I will briefly explain how the above results help to red
erive the quantum-classical duality between the trigonometric degeneration
s of the considered integrable systems and the corresponding spin chains\,
as well as shed some light on the spectral duality for them.\n
LOCATION:https://researchseminars.org/talk/M-seminar/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amina Abdurrahman (IHES)
DTSTART:20241205T190000Z
DTEND:20241205T200000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/150
DESCRIPTION:Title: Hyperbolic homology 3-spheres\, spectral gaps and torsion homology gro
wth\nby Amina Abdurrahman (IHES) as part of M-seminar\n\n\nAbstract\nW
hen does a sequence of hyperbolic 3-manifolds with volume going to infinit
y have exponentially growing torsion homology? For arithmetic towers\, the
work of Bergeron-Sengun-Venkatesh suggests a set of conditions that conje
cturally imply exponential growth of torsion homology. Their work relies o
n Cheeger-Mueller's theorem\, linking torsion homology and analytic torsio
n. For nice sequences of hyperbolic 3-manifolds we use a different approac
h to find a condition implying exponential torsion homology growth: we giv
e a condition on the spectrum of the Laplacian. I will give several motiva
tions for this condition and show how to construct concrete examples of se
quences satisfying it. This is based on joint work with Anshul Adve\, Vikr
am Giri\, Ben Lowe and Jonathan Zung.\n
LOCATION:https://researchseminars.org/talk/M-seminar/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Markarian (University of Strasbourg)
DTSTART:20250206T160000Z
DTEND:20250206T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/151
DESCRIPTION:Title: Multiplicative convolution and double shuffle relations\nby Nikita
Markarian (University of Strasbourg) as part of M-seminar\n\n\nAbstract\n
Multiple zeta values (and their motivic version) is the gadget lying in th
e heart of many subjects\, such as mixed Tate motives over Z.\nThe geometr
ic relations between them are\, therefore\, crucial for these subjects. Th
e associator relations are supposed to be the strongest among all relation
s. Regularized double shuffle relations form another set of relations. The
interaction between these two sets seems to be an important question. Del
igne and Terasoma initiated a geometric approach to interpreting regulariz
ed double shuffle relations. This approach explains the form of these rela
tions: group-likeness of a certain element of a Hopf algebra. The tensor c
ategory standing behind this Hopf algebra is a certain category built of p
erverse sheaves\, the tensor product being given by convolution. I will pr
esent my version of this approach\, which (in my opinion) clarifies and si
mplifies some points. The first part of this story is published as preprin
t https://arxiv.org/abs/2412.15694 .\n
LOCATION:https://researchseminars.org/talk/M-seminar/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nikolaev (University of Birmingham)
DTSTART:20250213T160000Z
DTEND:20250213T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/152
DESCRIPTION:Title: Geometry and Resurgence of WKB Solutions of Schrödinger Equations - P
art 1\nby Nikita Nikolaev (University of Birmingham) as part of M-semi
nar\n\n\nAbstract\nI will recall the WKB method for Schrödinger equations
and explain how to make sense of it in more invariant and geometric terms
. I will then explain how to prove that Schrödinger equations on compact
Riemann surfaces have the so-called quantum resurgence property: the Borel
transform of a formal WKB solution is a holomorphic germ that extends to
a global holomorphic function on an infinite Riemann surface with exponent
ial bounds at infinity. This infinite Riemann surface has a rich geometry
that is built out of the geometry of the spectral curve and completely gov
erns the Stokes phenomenon in the WKB method. Based on arXiv:2410.17224.\n
LOCATION:https://researchseminars.org/talk/M-seminar/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nikolaev (University of Birmingham)
DTSTART:20250220T160000Z
DTEND:20250220T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/153
DESCRIPTION:Title: Geometry and Resurgence of WKB Solutions of Schrödinger Equations - P
art 2\nby Nikita Nikolaev (University of Birmingham) as part of M-semi
nar\n\n\nAbstract\nI will recall the WKB method for Schrödinger equations
and explain how to make sense of it in more invariant and geometric terms
. I will then explain how to prove that Schrödinger equations on compact
Riemann surfaces have the so-called quantum resurgence property: the Borel
transform of a formal WKB solution is a holomorphic germ that extends to
a global holomorphic function on an infinite Riemann surface with exponent
ial bounds at infinity. This infinite Riemann surface has a rich geometry
that is built out of the geometry of the spectral curve and completely gov
erns the Stokes phenomenon in the WKB method. Based on arXiv:2410.17224.\n
LOCATION:https://researchseminars.org/talk/M-seminar/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanski (MIT)
DTSTART:20250227T160000Z
DTEND:20250227T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/154
DESCRIPTION:Title: From quantum loop group to coherent Satake category via fusion product
\nby Ilya Dumanski (MIT) as part of M-seminar\n\n\nAbstract\nCautis an
d Williams considered the category of perverse coherent sheaves on the aff
ine Grassmanian and proved for GL and conjectured for other types that thi
s category has a cluster structure. I will speak about partial progress to
wards the proof of this conjecture for simply-laced types. Our approach is
based on relating the coherent Satake category with the category of finit
e-dimensional modules over the affine quantum group. The bridge between th
ese two categories is provided by the notion of Feigin-Loktev fusion produ
ct for modules over the current algebra. In particular\, it helps to const
ruct cluster short exact sequences of perverse coherent sheaves using the
existence of exact sequences of modules over the quantum affine group\, ca
lled the Q-systems.\n
LOCATION:https://researchseminars.org/talk/M-seminar/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics)
DTSTART:20250306T160000Z
DTEND:20250306T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/155
DESCRIPTION:Title: Counting in Calabi-Yau categories - Part 1\nby Fabian Haiden (Cent
er for Quantum Mathematics) as part of M-seminar\n\n\nAbstract\nI will dis
cuss a replacement for homotopy cardinality in situations where it is a pr
iori ill-defined\, including Z/2-graded dg-categories. A key ingredient ar
e Calabi-Yau structures and their relative generalizations. As an applicat
ion we obtain a Hall algebra for many pre-triangulated dg-categories for w
hich it was previously undefined. This also gives an intrinsic replacement
for many ad-hoc constructions\, such as that of the elliptic Hall algebra
via the Drinfeld double. Another application is the proof of a conjecture
of Ng-Rutherford-Shende-Sivek expressing the ruling polynomial of a Z/2m-
graded Legendrian knot (which is part of the HOMFLY polynomial if m=1) in
terms of the homotopy cardinality of its augmentation category. This is jo
int work with Mikhail Gorsky\, arxiv:2409.10154.\n
LOCATION:https://researchseminars.org/talk/M-seminar/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Center for Quantum Mathematics)
DTSTART:20250313T160000Z
DTEND:20250313T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/156
DESCRIPTION:Title: Counting in Calabi-Yau categories - Part 2\nby Fabian Haiden (Cent
er for Quantum Mathematics) as part of M-seminar\n\n\nAbstract\nI will dis
cuss a replacement for homotopy cardinality in situations where it is a pr
iori ill-defined\, including Z/2-graded dg-categories. A key ingredient ar
e Calabi-Yau structures and their relative generalizations. As an applicat
ion we obtain a Hall algebra for many pre-triangulated dg-categories for w
hich it was previously undefined. This also gives an intrinsic replacement
for many ad-hoc constructions\, such as that of the elliptic Hall algebra
via the Drinfeld double. Another application is the proof of a conjecture
of Ng-Rutherford-Shende-Sivek expressing the ruling polynomial of a Z/2m-
graded Legendrian knot (which is part of the HOMFLY polynomial if m=1) in
terms of the homotopy cardinality of its augmentation category. This is jo
int work with Mikhail Gorsky\, arxiv:2409.10154.\n
LOCATION:https://researchseminars.org/talk/M-seminar/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Haney (Columbia University)
DTSTART:20250327T203000Z
DTEND:20250327T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/157
DESCRIPTION:Title: Infinity inner products and open Gromov-Witten invariants\nby Seba
stian Haney (Columbia University) as part of M-seminar\n\n\nAbstract\nThe
open Gromov-Witten (OGW) potential is a function defined on the Maurer-Car
tan space of a closed Lagrangian submanifold in a symplectic manifold with
values in the Novikov ring. From the values of the OGW potential\, one ca
n extract so-called open Gromov-Witten invariants\, which count pseudoholo
morphic disks with boundary on the Lagrangian. Standard definitions of the
OGW potential only allow for the construction of OGW invariants with valu
es in the real or complex numbers. In this talk\, we will present a constr
uction of the OGW potential which gives invariants valued in any field of
characteristic zero. The main algebraic input for our construction is a ho
motopy cyclic inner product on the (curved) Fukaya A-infinity algebra\, wh
ich generalizes the notion of a cyclically symmetric inner product and is
determined by a strong proper Calabi-Yau structure on the Fukaya category.
\n
LOCATION:https://researchseminars.org/talk/M-seminar/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martijn Kool (Utrecht University)
DTSTART:20250403T150000Z
DTEND:20250403T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/158
DESCRIPTION:Title: Virtual structure on Hilbert schemes of affine 4-space\nby Martijn
Kool (Utrecht University) as part of M-seminar\n\n\nAbstract\nWe consider
the generating series of certain K-theoretic invariants of Hilbert scheme
s of points on affine 4-space. Using torus localization\, it reduces to an
interesting weighted count of solid partitions for which Nekrasov provide
d a (conjectural) closed formula. We prove this formula by showing that th
e K-theoretic insertions lift to spin modules and give rise to a factoriza
ble sequence of sheaves in the sense of Okounkov. Time permitting\, we dis
cuss relations to Nekrasov’s origami gauge theory.\n
LOCATION:https://researchseminars.org/talk/M-seminar/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenjun Niu (Perimeter Institute)
DTSTART:20250409T150000Z
DTEND:20250409T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/159
DESCRIPTION:Title: Quantum algebras and spectral R-matrices from equivariant affine Grass
mannians - Part 1\nby Wenjun Niu (Perimeter Institute) as part of M-se
minar\n\n\nAbstract\nIn these two talks I will explain my joint work with
R. Abedin\, in which we construct new quantum algebras and spectral soluti
ons of quantum Yang-Baxter equations. These quantum algebras are quantizat
ions of Yang’s r matrix associated to the cotangent Lie algebra d=T^*g o
f a Lie algebra g. Our construction is based on the geometry of the equiva
riant affine Grassmannian associated to g\, and is related to holomorphic-
topological twist of 4d N=2 gauge theories. I will start by giving a brief
review of the holomorphic-topological twist of 4d N=2 gauge theories\, es
pecially its relation to equivariant affine Grassmannians. I will also rev
iew the work of Costello-Witten-Yamazaki\, in which the authors give a gau
ge-theoretic origin to spectral solutions of YB equations. Our constructio
ns are inspired by these physical considerations. After that\, I will expl
ain our results in relation to the geometry of equivariant affine Grassman
nians. Time permitting\, I will also explain how we can dynamically twist
the quantum algebra over formal neighborhoods of the moduli space of G-bun
dles\, and obtain dynamical R-matrices as a consequence.\n
LOCATION:https://researchseminars.org/talk/M-seminar/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenjun Niu (Perimeter Institute)
DTSTART:20250416T150000Z
DTEND:20250416T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/160
DESCRIPTION:Title: Quantum algebras and spectral R-matrices from equivariant affine Grass
mannians - Part 2\nby Wenjun Niu (Perimeter Institute) as part of M-se
minar\n\n\nAbstract\nIn these two talks I will explain my joint work with
R. Abedin\, in which we construct new quantum algebras and spectral soluti
ons of quantum Yang-Baxter equations. These quantum algebras are quantizat
ions of Yang’s r matrix associated to the cotangent Lie algebra d=T^*g o
f a Lie algebra g. Our construction is based on the geometry of the equiva
riant affine Grassmannian associated to g\, and is related to holomorphic-
topological twist of 4d N=2 gauge theories. I will start by giving a brief
review of the holomorphic-topological twist of 4d N=2 gauge theories\, es
pecially its relation to equivariant affine Grassmannians. I will also rev
iew the work of Costello-Witten-Yamazaki\, in which the authors give a gau
ge-theoretic origin to spectral solutions of YB equations. Our constructio
ns are inspired by these physical considerations. After that\, I will expl
ain our results in relation to the geometry of equivariant affine Grassman
nians. Time permitting\, I will also explain how we can dynamically twist
the quantum algebra over formal neighborhoods of the moduli space of G-bun
dles\, and obtain dynamical R-matrices as a consequence.\n
LOCATION:https://researchseminars.org/talk/M-seminar/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Joyce (University of Oxford)
DTSTART:20250424T150000Z
DTEND:20250424T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/161
DESCRIPTION:Title: Orientations on moduli spaces of coherent sheaves on Calabi-Yau 4-fold
s - Part I\nby Dominic Joyce (University of Oxford) as part of M-semin
ar\n\n\nAbstract\nLet X be a compact Calabi-Yau 4-fold. To define DT4 inva
riants of X\, one needs an orientation on moduli spaces of semistable cohe
rent sheaves on X\, or (better) an orientation on the moduli stack M of al
l perfect complexes on X\, in the sense of Borisov-Joyce 2017. Cao-Gross-J
oyce 2020 claimed to prove that M is orientable for any Calabi-Yau 4-fold
X. Unfortunately\, we have found a mistake in their proof\, and the theore
m itself may be false\, though we do not have a counterexample. I will exp
lain how to fix the mistake in Cao-Gross-Joyce under an extra hypothesis o
n the cohomology H^3(X\,Z) (for example\, H^3(X\,Z)=0 is sufficient). We a
lso explain a choice of extra data (a "flag structure” on H^4(X\,Z)) whi
ch determines a canonical orientation on M. This is part of a larger proje
ct studying orientability and orientations of moduli spaces of connections
in gauge theory\, and of moduli spaces of special submanifolds. We define
"bordism categories” Bord_n(BG) with objects pairs (X\,P) of a compact
spin n-manifold X and a principal G-bundle P —> X. Then orientations of
gauge theory moduli spaces of connections on P can be encoded in a functor
from Bord_n(BG) to Z_2-torsors\, and an orientation of the gauge theory m
oduli space B_P corresponds to a trivialization of this functor on a subca
tegory [X\,P] of Bord_n(BG). It turns out that Bord_n(BG) is a "Picard gro
upoid”\, and can be understood in terms of the spin bordism groups Omega
_m^{Spin}(BG) for m=n\,n+1. So we reduce orientability questions to (diffi
cult) calculations involving spin bordism groups of classifying spaces in
Algebraic Topology. This is joint work with Markus Upmeier.\n
LOCATION:https://researchseminars.org/talk/M-seminar/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Joyce (University of Oxford)
DTSTART:20250501T150000Z
DTEND:20250501T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/162
DESCRIPTION:Title: Orientations on moduli spaces of coherent sheaves on Calabi-Yau 4-fold
s - Part II\nby Dominic Joyce (University of Oxford) as part of M-semi
nar\n\n\nAbstract\nLet X be a compact Calabi-Yau 4-fold. To define DT4 inv
ariants of X\, one needs an orientation on moduli spaces of semistable coh
erent sheaves on X\, or (better) an orientation on the moduli stack M of a
ll perfect complexes on X\, in the sense of Borisov-Joyce 2017. Cao-Gross-
Joyce 2020 claimed to prove that M is orientable for any Calabi-Yau 4-fold
X. Unfortunately\, we have found a mistake in their proof\, and the theor
em itself may be false\, though we do not have a counterexample. I will ex
plain how to fix the mistake in Cao-Gross-Joyce under an extra hypothesis
on the cohomology H^3(X\,Z) (for example\, H^3(X\,Z)=0 is sufficient). We
also explain a choice of extra data (a "flag structure” on H^4(X\,Z)) wh
ich determines a canonical orientation on M. This is part of a larger proj
ect studying orientability and orientations of moduli spaces of connection
s in gauge theory\, and of moduli spaces of special submanifolds. We defin
e "bordism categories” Bord_n(BG) with objects pairs (X\,P) of a compact
spin n-manifold X and a principal G-bundle P —> X. Then orientations of
gauge theory moduli spaces of connections on P can be encoded in a functo
r from Bord_n(BG) to Z_2-torsors\, and an orientation of the gauge theory
moduli space B_P corresponds to a trivialization of this functor on a subc
ategory [X\,P] of Bord_n(BG). It turns out that Bord_n(BG) is a "Picard gr
oupoid”\, and can be understood in terms of the spin bordism groups Omeg
a_m^{Spin}(BG) for m=n\,n+1. So we reduce orientability questions to (diff
icult) calculations involving spin bordism groups of classifying spaces in
Algebraic Topology. This is joint work with Markus Upmeier.\n
LOCATION:https://researchseminars.org/talk/M-seminar/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ailsa Keating (University of Cambridge)
DTSTART:20250508T150000Z
DTEND:20250508T160000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/163
DESCRIPTION:Title: Homological mirror symmetry for projective K3 surfaces\nby Ailsa K
eating (University of Cambridge) as part of M-seminar\n\n\nAbstract\nJoint
work with Paul Hacking. We outline a proof that the Fukaya category of a
projective K3 surface is equivalent to the derived category of coherent sh
eaves on the mirror\, which is a K3 surface of Picard rank 19 over the fie
ld C((q)) of formal Laurent series. This builds on prior work of Seidel\,
who proved the theorem in the case of the quartic surface\, Gross-Siebert\
, Kontsevich-Soibelman\, Sheridan\, and others.\n
LOCATION:https://researchseminars.org/talk/M-seminar/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yash Deshmukh (IAS)
DTSTART:20251002T203000Z
DTEND:20251002T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/164
DESCRIPTION:Title: Categorical and geometric enumerative invariants\nby Yash Deshmukh
(IAS) as part of M-seminar\n\n\nAbstract\nCostello introduced categorical
enumerative invariants for a smooth and proper Calabi--Yau category equip
ped with a splitting of the non-commutative Hodge--de Rham spectral sequen
ce. I will discuss an extension of this to a chain-level CohFT structure o
n the Hochschild homology of the category. This construction will be unive
rsal in a precise sense\, and I will explain how to exploit this to compar
e the categorical CohFT of a Fukaya category with the geometric CohFT of t
he underlying symplectic manifold whenever a chain-level open-closed Gromo
v--Witten CohFT satisfying suitable properties exists.\n
LOCATION:https://researchseminars.org/talk/M-seminar/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Descombes (Imperial College)
DTSTART:20251006T173000Z
DTEND:20251006T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/165
DESCRIPTION:Title: Hyperbolic localization in Donaldson-Thomas theory - 1\nby Pierre
Descombes (Imperial College) as part of M-seminar\n\n\nAbstract\nGiven a s
cheme X with an action of a one-dimensional torus\, the hyperbolic localiz
ation functor\, which restricts constructible complexes from X to the attr
acting variety X^+ and then projects with compact support to the fixed var
iety X^0\, was introduced by Braden in order to study generalizations of B
iałynicki-Birula decompositions beyond the smooth case. Richarz has then
proven that this functor commutes with vanishing cycles.\nUsing shifted sy
mplectic geometry and a shifted Darboux theorem\, moduli spaces of sheaves
on Calabi-Yau threefolds are described locally by critical loci of functi
ons on smooth spaces\, which are related locally by adding quadratic forms
to the functions. On such moduli spaces\, a DT perverse sheaf\, whose coh
omology gives the cohomological DT invariants\, was defined by Brav\, Buss
i\, Dupont\, Joyce\, and Szendroï by gluing vanishing cycles on such loca
l models\, involving a subtle trivialization of the action of quadratic fo
rms using orientation data.\nWe will explain here how to prove a formula f
or the hyperbolic localization of the DT perverse sheaf\, combining the re
sults of Białynicki-Birula and Richarz with a study of the behavior of hy
perbolic localization with quadratic forms and orientations. One obtains i
n particular from this result a critical version of Białynicki-Birula dec
omposition in cohomological DT theory.\nWe will also explain how to obtain
a stacky version of the above result\, replacing X^+ and X^0 by the stack
s of filtered and graded points\, which has recently led to the proof of f
undamental results in DT theory\, namely the proof of the Kontsevich-Soibe
lman wall-crossing formula and the construction of the cohomological Hall
algebra for CY3 categories.\n
LOCATION:https://researchseminars.org/talk/M-seminar/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Descombes (Imperial College)
DTSTART:20251008T173000Z
DTEND:20251008T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/166
DESCRIPTION:Title: Hyperbolic localization in Donaldson-Thomas theory - 2\nby Pierre
Descombes (Imperial College) as part of M-seminar\n\n\nAbstract\nGiven a s
cheme X with an action of a one-dimensional torus\, the hyperbolic localiz
ation functor\, which restricts constructible complexes from X to the attr
acting variety X^+ and then projects with compact support to the fixed var
iety X^0\, was introduced by Braden in order to study generalizations of B
iałynicki-Birula decompositions beyond the smooth case. Richarz has then
proven that this functor commutes with vanishing cycles.\nUsing shifted sy
mplectic geometry and a shifted Darboux theorem\, moduli spaces of sheaves
on Calabi-Yau threefolds are described locally by critical loci of functi
ons on smooth spaces\, which are related locally by adding quadratic forms
to the functions. On such moduli spaces\, a DT perverse sheaf\, whose coh
omology gives the cohomological DT invariants\, was defined by Brav\, Buss
i\, Dupont\, Joyce\, and Szendroï by gluing vanishing cycles on such loca
l models\, involving a subtle trivialization of the action of quadratic fo
rms using orientation data.\nWe will explain here how to prove a formula f
or the hyperbolic localization of the DT perverse sheaf\, combining the re
sults of Białynicki-Birula and Richarz with a study of the behavior of hy
perbolic localization with quadratic forms and orientations. One obtains i
n particular from this result a critical version of Białynicki-Birula dec
omposition in cohomological DT theory.\nWe will also explain how to obtain
a stacky version of the above result\, replacing X^+ and X^0 by the stack
s of filtered and graded points\, which has recently led to the proof of f
undamental results in DT theory\, namely the proof of the Kontsevich-Soibe
lman wall-crossing formula and the construction of the cohomological Hall
algebra for CY3 categories.\n
LOCATION:https://researchseminars.org/talk/M-seminar/166/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Descombes (Imperial College)
DTSTART:20251009T173000Z
DTEND:20251009T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/167
DESCRIPTION:Title: Hyperbolic localization in Donaldson-Thomas theory - 3\nby Pierre
Descombes (Imperial College) as part of M-seminar\n\n\nAbstract\nGiven a s
cheme X with an action of a one-dimensional torus\, the hyperbolic localiz
ation functor\, which restricts constructible complexes from X to the attr
acting variety X^+ and then projects with compact support to the fixed var
iety X^0\, was introduced by Braden in order to study generalizations of B
iałynicki-Birula decompositions beyond the smooth case. Richarz has then
proven that this functor commutes with vanishing cycles.\nUsing shifted sy
mplectic geometry and a shifted Darboux theorem\, moduli spaces of sheaves
on Calabi-Yau threefolds are described locally by critical loci of functi
ons on smooth spaces\, which are related locally by adding quadratic forms
to the functions. On such moduli spaces\, a DT perverse sheaf\, whose coh
omology gives the cohomological DT invariants\, was defined by Brav\, Buss
i\, Dupont\, Joyce\, and Szendroï by gluing vanishing cycles on such loca
l models\, involving a subtle trivialization of the action of quadratic fo
rms using orientation data.\nWe will explain here how to prove a formula f
or the hyperbolic localization of the DT perverse sheaf\, combining the re
sults of Białynicki-Birula and Richarz with a study of the behavior of hy
perbolic localization with quadratic forms and orientations. One obtains i
n particular from this result a critical version of Białynicki-Birula dec
omposition in cohomological DT theory.\nWe will also explain how to obtain
a stacky version of the above result\, replacing X^+ and X^0 by the stack
s of filtered and graded points\, which has recently led to the proof of f
undamental results in DT theory\, namely the proof of the Kontsevich-Soibe
lman wall-crossing formula and the construction of the cohomological Hall
algebra for CY3 categories.\n
LOCATION:https://researchseminars.org/talk/M-seminar/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabin Cautis (UBC)
DTSTART:20251014T210000Z
DTEND:20251014T220000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/168
DESCRIPTION:Title: Abelian Hall categories - 1\nby Sabin Cautis (UBC) as part of M-se
minar\n\n\nAbstract\nAfter reviewing some background\, we will explain how
to associate to any\nquiver a finite length abelian category which catego
rifies the corresponding K-theoretic Hall algebra. The simples in this cat
egory provide a (dual) canonical basis of the Hall algebra. In particular\
, if the quiver is affine\, this provides a basis for the positive half of
the corresponding quantum toroidal algebra. We also explain how this abel
ian category is naturally endowed with renormalized r-matrices.\n
LOCATION:https://researchseminars.org/talk/M-seminar/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabin Cautis (UBC)
DTSTART:20251015T210000Z
DTEND:20251015T220000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/169
DESCRIPTION:Title: Abelian Hall categories - 2\nby Sabin Cautis (UBC) as part of M-se
minar\n\n\nAbstract\nAfter reviewing some background\, we will explain how
to associate to any\nquiver a finite length abelian category which catego
rifies the corresponding K-theoretic Hall algebra. The simples in this cat
egory provide a (dual) canonical basis of the Hall algebra. In particular\
, if the quiver is affine\, this provides a basis for the positive half of
the corresponding quantum toroidal algebra. We also explain how this abel
ian category is naturally endowed with renormalized r-matrices.\n
LOCATION:https://researchseminars.org/talk/M-seminar/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabin Cautis (UBC)
DTSTART:20251016T210000Z
DTEND:20251016T220000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/170
DESCRIPTION:Title: Abelian Hall categories - 3\nby Sabin Cautis (UBC) as part of M-se
minar\n\n\nAbstract\nAfter reviewing some background\, we will explain how
to associate to any\nquiver a finite length abelian category which catego
rifies the corresponding K-theoretic Hall algebra. The simples in this cat
egory provide a (dual) canonical basis of the Hall algebra. In particular\
, if the quiver is affine\, this provides a basis for the positive half of
the corresponding quantum toroidal algebra. We also explain how this abel
ian category is naturally endowed with renormalized r-matrices.\n
LOCATION:https://researchseminars.org/talk/M-seminar/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiu-Chu Melissa Liu (Columbia University)
DTSTART:20251023T203000Z
DTEND:20251023T213000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/171
DESCRIPTION:Title: Remodeling Conjecture with descendants\nby Chiu-Chu Melissa Liu (C
olumbia University) as part of M-seminar\n\n\nAbstract\nThe Remodeling Con
jecture proposed by Bouchard-Klemm-Mariño-Pasquetti relates Gromov-Witten
(GW) invariants counting holomorphic curves in a toric Calabi-Yau 3-manif
old/3-orbifold to the Chekhov-Eynard-Orantin Topological Recursion (TR) in
variants of its mirror curve. In this talk\, I will describe the Remodelin
g Conjecture with descendants\, which is a correspondence between all-genu
s equivariant descendant GW invariants and oscillatory integrals (Laplace
transforms) of TR invariants along relative 1-cycles on the equivariant mi
rror curve. Our genus-zero correspondence is a version of equivariant Hodg
e-theoretic mirror symmetry with integral structures. In the non-equivaria
nt setting\, we prove a conjecture of Hosono which equates quantum cohomol
ogy central charges of compactly supported coherent sheaves with period in
tegrals of a holomorphic 3-form along integral 3-cycles on the Hori-Vafa m
irror. This talk is based on joint work with Bohan Fang\, Song Yu\, and Zh
engyu Zong.\n
LOCATION:https://researchseminars.org/talk/M-seminar/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Yue Yu (CalTech)
DTSTART:20251030T200000Z
DTEND:20251030T210000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/172
DESCRIPTION:by Tony Yue Yu (CalTech) as part of M-seminar\n\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/M-seminar/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruoxi Li (University of Pittsburgh)
DTSTART:20251106T213000Z
DTEND:20251106T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/173
DESCRIPTION:Title: Motivic classes of varieties and stacks with applications to Higgs bun
dles and bundles with connections\nby Ruoxi Li (University of Pittsbur
gh) as part of M-seminar\n\n\nAbstract\nIn this talk\, we will first discu
ss the motivations for motivic classes coming from point counting over fin
ite fields. Then we will give the definitions of the motivic classes of va
rieties\, in particular we explain that an extra relation is needed in fin
ite characteristic. We will introduce symmetric powers and motivic zeta fu
nctions that are universal versions of local zeta functions.\nFor the seco
nd part of the talk\, we will focus on the motivic classes of stacks. In p
articular\, we will give the explicit formulas for the motivic classes of
moduli of Higgs bundles. If time permits\, we will discuss future work on
the motivic classes of moduli of bundles with connections.\n
LOCATION:https://researchseminars.org/talk/M-seminar/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Alexandrov (Université de Montpellier)
DTSTART:20251110T160000Z
DTEND:20251110T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/174
DESCRIPTION:Title: Mock modularity of Calabi-Yau threefolds - 1\nby Sergey Alexandrov
(Université de Montpellier) as part of M-seminar\n\n\nAbstract\nThe semi
nars aim to explain modular properties of rank 0 generalized Donaldson-Tho
mas (DT) invariants\, how these properties can be used to compute the inva
riants\, and their implications for other topological invariants such as V
afa-Witten and Gopakumar-Vafa.\n\n1. In the first part\, I'll explain basi
c facts about modular forms\, mock modular forms\, Jacobi forms and indefi
nite theta series. In the end\, I'll switch the topic and explain a few fa
cts about generalized DT invariants associated to Calabi-Yau threefolds.\n
\n2. In the second part\, I'll explain how one can derive precise modular
properties of the generating functions of rank 0 DT invariants which turn
out to be (higher depth) mock modular forms. I'll present an equation enco
ding the modular anomaly\, its extensions and how it can be solved for com
pact and non-compact CY threefolds.\n\n3. In the compact case\, the soluti
on of the modular anomaly allows us to fix the generating functions up to
a finite number of coefficients\, the so-called polar terms. In the third
part\, I'll show how these terms can be computed using wall-crossing and d
irect integration of topological string\, which for a set of compact one-p
arameter threefolds resulted in explicit modular and mock modular forms en
coding rank 0 DT invariants. In turn\, they have been used to generate new
Gopakumar-Vafa invariants overcoming the limitations of the direct integr
ation method.\n
LOCATION:https://researchseminars.org/talk/M-seminar/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Alexandrov (Université de Montpellier)
DTSTART:20251112T160000Z
DTEND:20251112T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/175
DESCRIPTION:Title: Mock modularity of Calabi-Yau threefolds - 2\nby Sergey Alexandrov
(Université de Montpellier) as part of M-seminar\n\n\nAbstract\nThe semi
nars aim to explain modular properties of rank 0 generalized Donaldson-Tho
mas (DT) invariants\, how these properties can be used to compute the inva
riants\, and their implications for other topological invariants such as V
afa-Witten and Gopakumar-Vafa.\n\n1. In the first part\, I'll explain basi
c facts about modular forms\, mock modular forms\, Jacobi forms and indefi
nite theta series. In the end\, I'll switch the topic and explain a few fa
cts about generalized DT invariants associated to Calabi-Yau threefolds.\n
\n2. In the second part\, I'll explain how one can derive precise modular
properties of the generating functions of rank 0 DT invariants which turn
out to be (higher depth) mock modular forms. I'll present an equation enco
ding the modular anomaly\, its extensions and how it can be solved for com
pact and non-compact CY threefolds.\n\n3. In the compact case\, the soluti
on of the modular anomaly allows us to fix the generating functions up to
a finite number of coefficients\, the so-called polar terms. In the third
part\, I'll show how these terms can be computed using wall-crossing and d
irect integration of topological string\, which for a set of compact one-p
arameter threefolds resulted in explicit modular and mock modular forms en
coding rank 0 DT invariants. In turn\, they have been used to generate new
Gopakumar-Vafa invariants overcoming the limitations of the direct integr
ation method.\n
LOCATION:https://researchseminars.org/talk/M-seminar/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Alexandrov (Université de Montpellier)
DTSTART:20251113T160000Z
DTEND:20251113T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/176
DESCRIPTION:Title: Mock modularity of Calabi-Yau threefolds - 3\nby Sergey Alexandrov
(Université de Montpellier) as part of M-seminar\n\n\nAbstract\nThe semi
nars aim to explain modular properties of rank 0 generalized Donaldson-Tho
mas (DT) invariants\, how these properties can be used to compute the inva
riants\, and their implications for other topological invariants such as V
afa-Witten and Gopakumar-Vafa.\n\n1. In the first part\, I'll explain basi
c facts about modular forms\, mock modular forms\, Jacobi forms and indefi
nite theta series. In the end\, I'll switch the topic and explain a few fa
cts about generalized DT invariants associated to Calabi-Yau threefolds.\n
\n2. In the second part\, I'll explain how one can derive precise modular
properties of the generating functions of rank 0 DT invariants which turn
out to be (higher depth) mock modular forms. I'll present an equation enco
ding the modular anomaly\, its extensions and how it can be solved for com
pact and non-compact CY threefolds.\n\n3. In the compact case\, the soluti
on of the modular anomaly allows us to fix the generating functions up to
a finite number of coefficients\, the so-called polar terms. In the third
part\, I'll show how these terms can be computed using wall-crossing and d
irect integration of topological string\, which for a set of compact one-p
arameter threefolds resulted in explicit modular and mock modular forms en
coding rank 0 DT invariants. In turn\, they have been used to generate new
Gopakumar-Vafa invariants overcoming the limitations of the direct integr
ation method.\n
LOCATION:https://researchseminars.org/talk/M-seminar/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Institut de Mathématiques de Jussieu-Paris Rive
Gauche)
DTSTART:20251117T183000Z
DTEND:20251117T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/177
DESCRIPTION:Title: BPS cohomology and quasi-BPS categories (1 of 4)\nby Tudor Padurar
iu (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as part of M-
seminar\n\n\nAbstract\nBPS invariants were initially introduced as counts
of objects in Calabi-Yau 3-categories\, generalizing Donaldson-Thomas inva
riants counting ideal sheaves\, or stable sheaves (in the absence of stric
tly semistable sheaves) on a Calabi-Yau 3-fold. BPS invariants may be defi
ned more generally for symmetric stacks\, and they can be also refined to
BPS cohomology and (partially) to quasi-BPS categories. \nI will discuss t
he construction and some of the fundamental results about BPS cohomology a
nd quasi-BPS categories of symmetric stacks. I will focus mostly on the ca
se of quivers with potential and Higgs bundles on a curve. More precisely\
, I will talk about the construction of the Hall product in (singular or c
ritical) cohomology and for categories of coherent sheaves or matrix facto
rizations\, cohomological integrality\, semiorthogonal decompositions of r
elevant categories in terms of quasi-BPS categories\, and properties of qu
asi-BPS categories. Lastly\, I will discuss the \\chi-independence phenome
non for moduli of sheaves supported on curves in a Calabi-Yau 3-fold for b
oth BPS cohomology and quasi-BPS categories\, and its relation to mirror s
ymmetry and Langlands duality for local curves. \nThe results discussed ar
e due to many people\, including Kontsevich-Soibelman\, Joyce et.al\, Mein
hardt-Reineke\, Davison-Meinhardt\, Toda etc. I will also mention results
from joint work with Yukinobu Toda\, and joint work with Chenjing Bu\, Ben
Davison\, Andrés Ibáñez Núñez\, and Tasuki Kinjo.\n
LOCATION:https://researchseminars.org/talk/M-seminar/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Institut de Mathématiques de Jussieu-Paris Rive
Gauche)
DTSTART:20251118T173000Z
DTEND:20251118T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/178
DESCRIPTION:Title: BPS cohomology and quasi-BPS categories (2 of 4)\nby Tudor Padurar
iu (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as part of M-
seminar\n\n\nAbstract\nBPS invariants were initially introduced as counts
of objects in Calabi-Yau 3-categories\, generalizing Donaldson-Thomas inva
riants counting ideal sheaves\, or stable sheaves (in the absence of stric
tly semistable sheaves) on a Calabi-Yau 3-fold. BPS invariants may be defi
ned more generally for symmetric stacks\, and they can be also refined to
BPS cohomology and (partially) to quasi-BPS categories. \nI will discuss t
he construction and some of the fundamental results about BPS cohomology a
nd quasi-BPS categories of symmetric stacks. I will focus mostly on the ca
se of quivers with potential and Higgs bundles on a curve. More precisely\
, I will talk about the construction of the Hall product in (singular or c
ritical) cohomology and for categories of coherent sheaves or matrix facto
rizations\, cohomological integrality\, semiorthogonal decompositions of r
elevant categories in terms of quasi-BPS categories\, and properties of qu
asi-BPS categories. Lastly\, I will discuss the \\chi-independence phenome
non for moduli of sheaves supported on curves in a Calabi-Yau 3-fold for b
oth BPS cohomology and quasi-BPS categories\, and its relation to mirror s
ymmetry and Langlands duality for local curves. \nThe results discussed ar
e due to many people\, including Kontsevich-Soibelman\, Joyce et.al\, Mein
hardt-Reineke\, Davison-Meinhardt\, Toda etc. I will also mention results
from joint work with Yukinobu Toda\, and joint work with Chenjing Bu\, Ben
Davison\, Andrés Ibáñez Núñez\, and Tasuki Kinjo.\n
LOCATION:https://researchseminars.org/talk/M-seminar/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Institut de Mathématiques de Jussieu-Paris Rive
Gauche)
DTSTART:20251119T173000Z
DTEND:20251119T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/179
DESCRIPTION:Title: BPS cohomology and quasi-BPS categories (3 of 4)\nby Tudor Padurar
iu (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as part of M-
seminar\n\n\nAbstract\nBPS invariants were initially introduced as counts
of objects in Calabi-Yau 3-categories\, generalizing Donaldson-Thomas inva
riants counting ideal sheaves\, or stable sheaves (in the absence of stric
tly semistable sheaves) on a Calabi-Yau 3-fold. BPS invariants may be defi
ned more generally for symmetric stacks\, and they can be also refined to
BPS cohomology and (partially) to quasi-BPS categories. \nI will discuss t
he construction and some of the fundamental results about BPS cohomology a
nd quasi-BPS categories of symmetric stacks. I will focus mostly on the ca
se of quivers with potential and Higgs bundles on a curve. More precisely\
, I will talk about the construction of the Hall product in (singular or c
ritical) cohomology and for categories of coherent sheaves or matrix facto
rizations\, cohomological integrality\, semiorthogonal decompositions of r
elevant categories in terms of quasi-BPS categories\, and properties of qu
asi-BPS categories. Lastly\, I will discuss the \\chi-independence phenome
non for moduli of sheaves supported on curves in a Calabi-Yau 3-fold for b
oth BPS cohomology and quasi-BPS categories\, and its relation to mirror s
ymmetry and Langlands duality for local curves. \nThe results discussed ar
e due to many people\, including Kontsevich-Soibelman\, Joyce et.al\, Mein
hardt-Reineke\, Davison-Meinhardt\, Toda etc. I will also mention results
from joint work with Yukinobu Toda\, and joint work with Chenjing Bu\, Ben
Davison\, Andrés Ibáñez Núñez\, and Tasuki Kinjo.\n
LOCATION:https://researchseminars.org/talk/M-seminar/179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (Institut de Mathématiques de Jussieu-Paris Rive
Gauche)
DTSTART:20251120T173000Z
DTEND:20251120T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/180
DESCRIPTION:Title: BPS cohomology and quasi-BPS categories (4 of 4)\nby Tudor Padurar
iu (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as part of M-
seminar\n\n\nAbstract\nBPS invariants were initially introduced as counts
of objects in Calabi-Yau 3-categories\, generalizing Donaldson-Thomas inva
riants counting ideal sheaves\, or stable sheaves (in the absence of stric
tly semistable sheaves) on a Calabi-Yau 3-fold. BPS invariants may be defi
ned more generally for symmetric stacks\, and they can be also refined to
BPS cohomology and (partially) to quasi-BPS categories. \nI will discuss t
he construction and some of the fundamental results about BPS cohomology a
nd quasi-BPS categories of symmetric stacks. I will focus mostly on the ca
se of quivers with potential and Higgs bundles on a curve. More precisely\
, I will talk about the construction of the Hall product in (singular or c
ritical) cohomology and for categories of coherent sheaves or matrix facto
rizations\, cohomological integrality\, semiorthogonal decompositions of r
elevant categories in terms of quasi-BPS categories\, and properties of qu
asi-BPS categories. Lastly\, I will discuss the \\chi-independence phenome
non for moduli of sheaves supported on curves in a Calabi-Yau 3-fold for b
oth BPS cohomology and quasi-BPS categories\, and its relation to mirror s
ymmetry and Langlands duality for local curves. \nThe results discussed ar
e due to many people\, including Kontsevich-Soibelman\, Joyce et.al\, Mein
hardt-Reineke\, Davison-Meinhardt\, Toda etc. I will also mention results
from joint work with Yukinobu Toda\, and joint work with Chenjing Bu\, Ben
Davison\, Andrés Ibáñez Núñez\, and Tasuki Kinjo.\n
LOCATION:https://researchseminars.org/talk/M-seminar/180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina)
DTSTART:20251202T213000Z
DTEND:20251202T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/181
DESCRIPTION:Title: Frobenius structures for quantum differential and q-difference equatio
ns (1 of 3)\nby Andrey Smirnov (University of North Carolina) as part
of M-seminar\n\n\nAbstract\nThere is a known connection between the Kloost
erman sum in number theory and the Bessel differential equation. This conn
ection was explained by B. Dwork in 1974 through his discovery of Frobeniu
s structures in the p-adic theory of the Bessel equation. In this talk\, I
will speculate that this connection extends to the quantum differential e
quations appearing in the quantum cohomology of Nakajima varieties. As an
example\, I will present an explicit conjectural description of the corres
ponding Frobenius structures. The traces of these Frobenius structures ser
ve as natural finite-field analogs of the integral solutions to quantum di
fferential equations known from mirror symmetry. Some of these results als
o extend to the setting of q-difference equations\, where a similar pictur
e emerges when q is close to a root of unity in the p-adic norm. I will re
view these developments and discuss their connections to other recent adva
nces\, including quantum Steenrod operations\, Habiro cohomology\, and rel
ated topics.\n
LOCATION:https://researchseminars.org/talk/M-seminar/181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina)
DTSTART:20251203T213000Z
DTEND:20251203T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/182
DESCRIPTION:Title: Frobenius structures for quantum differential and q-difference equatio
ns (2 of 3)\nby Andrey Smirnov (University of North Carolina) as part
of M-seminar\n\n\nAbstract\nThere is a known connection between the Kloost
erman sum in number theory and the Bessel differential equation. This conn
ection was explained by B. Dwork in 1974 through his discovery of Frobeniu
s structures in the p-adic theory of the Bessel equation. In this talk\, I
will speculate that this connection extends to the quantum differential e
quations appearing in the quantum cohomology of Nakajima varieties. As an
example\, I will present an explicit conjectural description of the corres
ponding Frobenius structures. The traces of these Frobenius structures ser
ve as natural finite-field analogs of the integral solutions to quantum di
fferential equations known from mirror symmetry. Some of these results als
o extend to the setting of q-difference equations\, where a similar pictur
e emerges when q is close to a root of unity in the p-adic norm. I will re
view these developments and discuss their connections to other recent adva
nces\, including quantum Steenrod operations\, Habiro cohomology\, and rel
ated topics.\n
LOCATION:https://researchseminars.org/talk/M-seminar/182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina)
DTSTART:20251204T213000Z
DTEND:20251204T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/183
DESCRIPTION:Title: Frobenius structures for quantum differential and q-difference equatio
ns (3 of 3)\nby Andrey Smirnov (University of North Carolina) as part
of M-seminar\n\n\nAbstract\nThere is a known connection between the Kloost
erman sum in number theory and the Bessel differential equation. This conn
ection was explained by B. Dwork in 1974 through his discovery of Frobeniu
s structures in the p-adic theory of the Bessel equation. In this talk\, I
will speculate that this connection extends to the quantum differential e
quations appearing in the quantum cohomology of Nakajima varieties. As an
example\, I will present an explicit conjectural description of the corres
ponding Frobenius structures. The traces of these Frobenius structures ser
ve as natural finite-field analogs of the integral solutions to quantum di
fferential equations known from mirror symmetry. Some of these results als
o extend to the setting of q-difference equations\, where a similar pictur
e emerges when q is close to a root of unity in the p-adic norm. I will re
view these developments and discuss their connections to other recent adva
nces\, including quantum Steenrod operations\, Habiro cohomology\, and rel
ated topics.\n
LOCATION:https://researchseminars.org/talk/M-seminar/183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Sulkowski (University of Warsaw)
DTSTART:20251210T183000Z
DTEND:20251210T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/184
DESCRIPTION:Title: Symmetric quivers for 2d\, 3d and 4d theories and topological strings
(1 of 2)\nby Piotr Sulkowski (University of Warsaw) as part of M-semin
ar\n\n\nAbstract\nI will present how invariants of symmetric quivers captu
re various\nobservables of physical theories in 2\, 3 and 4 dimensions\, a
s well as of topological string theory. The observables in question includ
e or are immediately related to knot invariants\, (wild) BPS degeneracies
of 4d N=2 theories\, superconformal indices\, wall-crossing identities\, 2
d CFT or VOA characters\, LMOV invariants\, etc. Such a unifying role of s
ymmetric quivers is very useful and intriguing and calls for deeper\nunder
standing.\n
LOCATION:https://researchseminars.org/talk/M-seminar/184/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Sulkowski (University of Warsaw)
DTSTART:20251211T183000Z
DTEND:20251211T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/185
DESCRIPTION:Title: Symmetric quivers for 2d\, 3d and 4d theories and topological strings
(2 of 2)\nby Piotr Sulkowski (University of Warsaw) as part of M-semin
ar\n\n\nAbstract\nI will present how invariants of symmetric quivers captu
re various\nobservables of physical theories in 2\, 3 and 4 dimensions\, a
s well as of topological string theory. The observables in question includ
e or are immediately related to knot invariants\, (wild) BPS degeneracies
of 4d N=2 theories\, superconformal indices\, wall-crossing identities\, 2
d CFT or VOA characters\, LMOV invariants\, etc. Such a unifying role of s
ymmetric quivers is very useful and intriguing and calls for deeper\nunder
standing.\n
LOCATION:https://researchseminars.org/talk/M-seminar/185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Tsygan (Northwestern University)
DTSTART:20260205T213000Z
DTEND:20260205T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/186
DESCRIPTION:Title: The Gauss-Manin connection in noncommutative geometry\nby Boris Ts
ygan (Northwestern University) as part of M-seminar\n\n\nAbstract\nIn nonc
ommutative geometry\, a variety is replaced by an associative ring or\, mo
re generally\, by an appropriate version of a category\, and the De Rham c
ohomology is replaced by the periodic cyclic complex. As shown by Getzler\
, the periodic cyclic homology of a family of algebras carries a flat conn
ection\, which is analogous to the De Rham cohomology of a family of varie
ties carrying the Gauss-Manin connection. The structure living on the peri
odic cyclic complex (as opposed to homology) had been studied extensively\
, for example by Dolgushev\, Tamarkin and the author\, by Kontsevich and S
oibelman\, by Willwacher\, and others. The question was recently revisited
by the author and\, from a different perspective\, by Antieu. I will revi
ew the main results and concentrate on explicit formulas. Those formulas s
eem to have good convergence properties\, both p-adic and Archimedean\; al
so\, they bear intriguing resemblance to some known constructions from mat
hematical physics\, D-module theory\, and formal groups.\n
LOCATION:https://researchseminars.org/talk/M-seminar/186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanski (MIT)
DTSTART:20260209T183000Z
DTEND:20260209T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/187
DESCRIPTION:Title: Perverse coherent sheaves on symplectic singularities (part 1 of 3)\nby Ilya Dumanski (MIT) as part of M-seminar\n\n\nAbstract\nPerverse con
structible sheaves are ubiquitous in algebraic geometry and geometric repr
esentation theory. Bezrukavnikov introduced their coherent analog\, called
perverse coherent sheaves. For technical reasons\, there are essentially
two interesting examples when this notion is well-behaved: the nilpotent c
one and the affine Grassmannian. In both these cases\, this category is ve
ry meaningful and well-studied. It is related to modular representation th
eory\, local geometric Langlands\, line defects in 4d gauge theories\, and
cluster categorifications. We will discuss these questions and then prese
nt a generalization of this construction to an arbitrary Poisson variety w
ith finitely many symplectic leaves\, most notably the symplectic singular
ities. This may be seen as a step towards building the Kazhdan-Lusztig the
ory in this setting.\n
LOCATION:https://researchseminars.org/talk/M-seminar/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanski (MIT)
DTSTART:20260211T183000Z
DTEND:20260211T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/188
DESCRIPTION:Title: Perverse coherent sheaves on symplectic singularities (part 2 of 3)\nby Ilya Dumanski (MIT) as part of M-seminar\n\n\nAbstract\nPerverse con
structible sheaves are ubiquitous in algebraic geometry and geometric repr
esentation theory. Bezrukavnikov introduced their coherent analog\, called
perverse coherent sheaves. For technical reasons\, there are essentially
two interesting examples when this notion is well-behaved: the nilpotent c
one and the affine Grassmannian. In both these cases\, this category is ve
ry meaningful and well-studied. It is related to modular representation th
eory\, local geometric Langlands\, line defects in 4d gauge theories\, and
cluster categorifications. We will discuss these questions and then prese
nt a generalization of this construction to an arbitrary Poisson variety w
ith finitely many symplectic leaves\, most notably the symplectic singular
ities. This may be seen as a step towards building the Kazhdan-Lusztig the
ory in this setting.\n
LOCATION:https://researchseminars.org/talk/M-seminar/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanski (MIT)
DTSTART:20260212T213000Z
DTEND:20260212T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/189
DESCRIPTION:Title: Perverse coherent sheaves on symplectic singularities (part 3 of 3)\nby Ilya Dumanski (MIT) as part of M-seminar\n\n\nAbstract\nPerverse con
structible sheaves are ubiquitous in algebraic geometry and geometric repr
esentation theory. Bezrukavnikov introduced their coherent analog\, called
perverse coherent sheaves. For technical reasons\, there are essentially
two interesting examples when this notion is well-behaved: the nilpotent c
one and the affine Grassmannian. In both these cases\, this category is ve
ry meaningful and well-studied. It is related to modular representation th
eory\, local geometric Langlands\, line defects in 4d gauge theories\, and
cluster categorifications. We will discuss these questions and then prese
nt a generalization of this construction to an arbitrary Poisson variety w
ith finitely many symplectic leaves\, most notably the symplectic singular
ities. This may be seen as a step towards building the Kazhdan-Lusztig the
ory in this setting.\n
LOCATION:https://researchseminars.org/talk/M-seminar/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rina Anno (KSU)
DTSTART:20260226T213000Z
DTEND:20260226T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/190
DESCRIPTION:Title: The Hochschild homology of a noncommutative symmetric quotient stack\nby Rina Anno (KSU) as part of M-seminar\n\n\nAbstract\nFor a small DG
category $A$\, its symmetric power $S^nA$ may be considered a noncommutati
ve symmetric quotient stack of $A$. We establish an isomorphism between $\
\bigoplus HH_\\bullet(S^nA)$ and the symmetric algebra $S^*(HH_\\bullet(A)
\\otimes t k[t])$ by chaining explicit maps of complexes. These graded ve
ctor spaces being isomorphic has been established before by Baranovsky in
the commutative case and conjectured by Belmans\, Fu\, and Krug in the for
m that we prove it. The explicit nature of the isomorphism allows us to tr
ansfer a number of structures from the symmetric algebra to $\\bigoplus HH
_\\bullet(S^nA)$\, since the former is a Hopf algebra\, the Fock space for
the Heisenberg algebra of $A$\, and a $\\lambda$-ring. In this talk\, I w
ill go over (some of the) history of the results this one is building upon
\, describe the quasiisomorphism\, and compare the result to the (much mor
e studied) commutative case. This talk is based on a joint work with V. Ba
ranovsky and T. Logvinenko\, https://arxiv.org/abs/2512.25039\n
LOCATION:https://researchseminars.org/talk/M-seminar/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Gaiotto (Perimeter Institute)
DTSTART:20260302T183000Z
DTEND:20260302T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/191
DESCRIPTION:Title: The categorical 't Hooft expansion - part 1 of 3\nby Davide Gaiott
o (Perimeter Institute) as part of M-seminar\n\n\nAbstract\nThe 't Hooft e
xpansion is the key structure underlying dualities between gauge theories
of large matrices and string theories. I will review categorical aspects o
f the 't Hooft expansion\, matching the formal deformation space of certai
n ``fundamental modifications'' of the gauge theory to the formal deformat
ion space of a category of boundary conditions ("D-branes") for a 2d dg-TF
T\, to be identified with the world-volume theory for the string theory. I
will illustrate this by reviewing the holographic description of correlat
ion functions for a 2d chiral algebra/VOA deforming H^*(gl_N[A[z]]\;gl_N)
for a 2d CY algebra A\n
LOCATION:https://researchseminars.org/talk/M-seminar/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Gaiotto (Perimeter Institute)
DTSTART:20260304T183000Z
DTEND:20260304T193000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/192
DESCRIPTION:Title: The categorical 't Hooft expansion - part 2 of 3\nby Davide Gaiott
o (Perimeter Institute) as part of M-seminar\n\n\nAbstract\nThe 't Hooft e
xpansion is the key structure underlying dualities between gauge theories
of large matrices and string theories. I will review categorical aspects o
f the 't Hooft expansion\, matching the formal deformation space of certai
n ``fundamental modifications'' of the gauge theory to the formal deformat
ion space of a category of boundary conditions ("D-branes") for a 2d dg-TF
T\, to be identified with the world-volume theory for the string theory. I
will illustrate this by reviewing the holographic description of correlat
ion functions for a 2d chiral algebra/VOA deforming H^*(gl_N[A[z]]\;gl_N)
for a 2d CY algebra A\n
LOCATION:https://researchseminars.org/talk/M-seminar/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Gaiotto (Perimeter Institute)
DTSTART:20260305T213000Z
DTEND:20260305T223000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/193
DESCRIPTION:Title: The categorical 't Hooft expansion - part 3 of 3\nby Davide Gaiott
o (Perimeter Institute) as part of M-seminar\n\n\nAbstract\nThe 't Hooft e
xpansion is the key structure underlying dualities between gauge theories
of large matrices and string theories. I will review categorical aspects o
f the 't Hooft expansion\, matching the formal deformation space of certai
n ``fundamental modifications'' of the gauge theory to the formal deformat
ion space of a category of boundary conditions ("D-branes") for a 2d dg-TF
T\, to be identified with the world-volume theory for the string theory. I
will illustrate this by reviewing the holographic description of correlat
ion functions for a 2d chiral algebra/VOA deforming H^*(gl_N[A[z]]\;gl_N)
for a 2d CY algebra A\n
LOCATION:https://researchseminars.org/talk/M-seminar/193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART:20260309T173000Z
DTEND:20260309T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/194
DESCRIPTION:Title: Tannaka/Koszul duality and line operators - part 1 of 3\nby Tudor
Dimofte (University of Edinburgh) as part of M-seminar\n\n\nAbstract\nThes
e seminars will focus on the representing line operators in topological an
d/or holomorphic QFT’s\, from the perspective of categorical reconstruct
ion theory. In particular\, I’ll explain how fiber functors have several
natural constructions in QFT\, leading to field-theoretic incarnations of
Tannaka and Koszul duality (following my own work but also many others\,
in particular work of Costello and collaborators). In the first talk\, I
’ll set up a general QFT framework for reconstruction theory\, and discu
ss a basic application to constructing (generalized) quantum groups from 3
d TQFT’s. In the second talk\, I’ll consider 4d holomorphic-topologica
l theories. I’ll review the work of Costello-Yamazaki-Witten on Yangians
in 4d Chern-Simons theory\, and explain how to generalize this to see str
uctures such as Drinfeld coproducts. I’ll also generalize further to rel
ate line operators in 4d Seiberg-Witten theories to CoHA’s of BPS states
. In the final talk\, I’ll consider 3d holomorphic-topological theories\
, and derive a new structure that I call a “dg-shifted” Yangian.\n
LOCATION:https://researchseminars.org/talk/M-seminar/194/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART:20260311T173000Z
DTEND:20260311T183000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/195
DESCRIPTION:Title: Tannaka/Koszul duality and line operators - part 2 of 3\nby Tudor
Dimofte (University of Edinburgh) as part of M-seminar\n\n\nAbstract\nThes
e seminars will focus on the representing line operators in topological an
d/or holomorphic QFT’s\, from the perspective of categorical reconstruct
ion theory. In particular\, I’ll explain how fiber functors have several
natural constructions in QFT\, leading to field-theoretic incarnations of
Tannaka and Koszul duality (following my own work but also many others\,
in particular work of Costello and collaborators). In the first talk\, I
’ll set up a general QFT framework for reconstruction theory\, and discu
ss a basic application to constructing (generalized) quantum groups from 3
d TQFT’s. In the second talk\, I’ll consider 4d holomorphic-topologica
l theories. I’ll review the work of Costello-Yamazaki-Witten on Yangians
in 4d Chern-Simons theory\, and explain how to generalize this to see str
uctures such as Drinfeld coproducts. I’ll also generalize further to rel
ate line operators in 4d Seiberg-Witten theories to CoHA’s of BPS states
. In the final talk\, I’ll consider 3d holomorphic-topological theories\
, and derive a new structure that I call a “dg-shifted” Yangian.\n
LOCATION:https://researchseminars.org/talk/M-seminar/195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART:20260312T160000Z
DTEND:20260312T170000Z
DTSTAMP:20260315T025116Z
UID:M-seminar/196
DESCRIPTION:Title: Tannaka/Koszul duality and line operators - part 3 of 3\nby Tudor
Dimofte (University of Edinburgh) as part of M-seminar\n\n\nAbstract\nThes
e seminars will focus on the representing line operators in topological an
d/or holomorphic QFT’s\, from the perspective of categorical reconstruct
ion theory. In particular\, I’ll explain how fiber functors have several
natural constructions in QFT\, leading to field-theoretic incarnations of
Tannaka and Koszul duality (following my own work but also many others\,
in particular work of Costello and collaborators). In the first talk\, I
’ll set up a general QFT framework for reconstruction theory\, and discu
ss a basic application to constructing (generalized) quantum groups from 3
d TQFT’s. In the second talk\, I’ll consider 4d holomorphic-topologica
l theories. I’ll review the work of Costello-Yamazaki-Witten on Yangians
in 4d Chern-Simons theory\, and explain how to generalize this to see str
uctures such as Drinfeld coproducts. I’ll also generalize further to rel
ate line operators in 4d Seiberg-Witten theories to CoHA’s of BPS states
. In the final talk\, I’ll consider 3d holomorphic-topological theories\
, and derive a new structure that I call a “dg-shifted” Yangian.\n
LOCATION:https://researchseminars.org/talk/M-seminar/196/
END:VEVENT
END:VCALENDAR