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BEGIN:VEVENT
SUMMARY:Alexandru Oancea (Sorbonne\, Paris)
DTSTART:20200505T150000Z
DTEND:20200505T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/1
DESCRIPTION:Title: Duality for Rabinowitz-Floer homology\nby Alexandru Oancea (Sorbonne\
, Paris) as part of Free Mathematics Seminar\n\n\nAbstract\nI will explain
a duality theorem with products in Rabinowitz-Floer homology. This has a
bearing on string topology and explains a number of dualities that have be
en observed in that setting. Joint work in progress with Kai Cieliebak and
Nancy Hingston.\n
LOCATION:https://researchseminars.org/talk/Freemath/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny August (MPIM\, Bonn)
DTSTART:20200512T140000Z
DTEND:20200512T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/2
DESCRIPTION:Title: Stability for contraction algebras\nby Jenny August (MPIM\, Bonn) as
part of Free Mathematics Seminar\n\n\nAbstract\nFor a finite dimensional a
lgebra\, Bridgeland stability conditions can be viewed as a continuous gen
eralisation of tilting theory\, providing a geometric way to study the der
ived category. Describing this stability manifold is often very challengin
g but in this talk\, I’ll look at a special class of symmetric alge
bras whose tilting theory is very well behaved\, allowing us to describe t
he entire stability manifold of such an algebra. This is joint work with M
ichael Wemyss.\n
LOCATION:https://researchseminars.org/talk/Freemath/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Smirnov (ETH\, Zurich)
DTSTART:20200519T140000Z
DTEND:20200519T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/3
DESCRIPTION:Title: Isotopy problem for symplectic forms in the presence of an anti-holomorph
ic involution\nby Gleb Smirnov (ETH\, Zurich) as part of Free Mathemat
ics Seminar\n\n\nAbstract\nSuppose we are given an algebraic surface equip
ped with an anti-holomorphic involution. From the symplectic viewpoint\, a
natural question to ask is: are there cohomologous anti-invariant symplec
tic forms on this manifold which are not isotopic within anti-invariant fo
rms? And\, if so\, how many? During the talk\, we will look at a particula
rly simple case of complex quadrics and do some explicit computations.\n
LOCATION:https://researchseminars.org/talk/Freemath/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazushi Ueda (Univ of Tokyo\, Japan)
DTSTART:20200526T090000Z
DTEND:20200526T100000Z
DTSTAMP:20260422T225755Z
UID:Freemath/4
DESCRIPTION:Title: Noncommutative del Pezzo surfaces\nby Kazushi Ueda (Univ of Tokyo\, J
apan) as part of Free Mathematics Seminar\n\n\nAbstract\nIt is known after
the works of Artin-Tate-Van den Bergh and Bondal-Polishchuk that noncommu
tative deformations of the projective plane are classified by triples cons
isting of a cubic curve and two line bundles. Similarly\, Van den Bergh ga
ve a classification of noncommutative quadric surfaces in terms of quadrup
les consisting of (a degeneration of) an elliptic curve and three line bun
dles. In the talk\, I will discuss a joint work in progress with Tarig Abd
elgadir and Shinnosuke Okawa on classifications of noncommutative del Pezz
o surfaces.\n
LOCATION:https://researchseminars.org/talk/Freemath/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuhan Sun (Stony Brook)
DTSTART:20200609T140000Z
DTEND:20200609T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/5
DESCRIPTION:Title: Displacement energy of Lagrangian 3-spheres\nby Yuhan Sun (Stony Broo
k) as part of Free Mathematics Seminar\n\n\nAbstract\nWe study local and g
lobal Hamiltonian dynamical behaviours of some Lagrangian submanifolds nea
r a Lagrangian sphere S in a symplectic manifold X. When dim S = 2\, we sh
ow that there is a one-parameter family of Lagrangian tori near S\, which
are nondisplaceable in X. When dim S = 3\, we obtain a new estimate of the
displacement energy of S\, by estimating the displacement energy of a one
-parameter family of Lagrangian tori near S.\n
LOCATION:https://researchseminars.org/talk/Freemath/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Octav Cornea (Univ of Montreal)
DTSTART:20200602T140000Z
DTEND:20200602T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/6
DESCRIPTION:Title: Lagrangians\, surgery and rigidity\nby Octav Cornea (Univ of Montreal
) as part of Free Mathematics Seminar\n\n\nAbstract\nI will discuss a fram
ework for analyzing classes of Lagrangian submanifolds\nthat aims to endow
them with a metric structure. The tools involve certain Floer type\nmachi
nery for immersed Lagrangians. Part of the picture is a correspondence\nbe
tween certain cobordism categories endowed with surgery models and derived
\nFukaya categories. The talks is based on joint work with Paul Biran.\n
LOCATION:https://researchseminars.org/talk/Freemath/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kuznetsov (Steklov)
DTSTART:20200623T150000Z
DTEND:20200623T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/7
DESCRIPTION:Title: Residual categories and quantum cohomology\nby Alexander Kuznetsov (S
teklov) as part of Free Mathematics Seminar\n\n\nAbstract\nDubrovin's conj
ecture predicts that a smooth projective variety has a full exceptional co
llection in the derived category of coherent sheaves if and only if its bi
g quantum cohomology ring is generically semisimple. However\, the big qua
ntum cohomology is very hard to compute. We suggest a conjecture\, where t
he big quantum cohomology is replaced by the small quantum cohomology (whi
ch is much more easy to compute)\, and a full exceptional collection is re
placed by a semiorthogonal decomposition of a special form. We support thi
s conjecture by a number of examples provided by homogeneous varieties of
simple algebraic groups. This is a joint work with Maxim Smirnov.\n
LOCATION:https://researchseminars.org/talk/Freemath/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (IPMU)
DTSTART:20200616T090000Z
DTEND:20200616T100000Z
DTSTAMP:20260422T225755Z
UID:Freemath/8
DESCRIPTION:Title: Symplectic geometry of exact WKB analysis\nby Tatsuki Kuwagaki (IPMU)
as part of Free Mathematics Seminar\n\n\nAbstract\nA sheaf quantization i
s a sheaf associated to a Lagrangian brane. This sheaf conjecturally has i
nformation as much as Floer theory of the Lagrangian. On the other hand\,
exact WKB analysis is an analysis of differential equations containing \\h
bar (the Planck constant).\n\nIn this talk\, I will explain how to constru
ct a sheaf quantization over the Novikov ring of the spectral curve of an
\\hbar-differential equation by using exact WKB method. In the constructio
n\, one can see how (conjecturally) the convergence in WKB analysis is rel
ated to the convergence in Fukaya category. In degree 2\, there is an appl
ication to cluster theory: the sheaf quantization associates a cluster coo
rdinate which is the same as the Voros-Iwaki-Nakanishi-Fock-Goncharov coor
dinate. I will also mention about some relationships to Riemann-Hilbert co
rrespondence of D'Agnolo-Kashiwara and Kontsevich-Soibelman.\n
LOCATION:https://researchseminars.org/talk/Freemath/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Sheridan (Edinburgh)
DTSTART:20200630T140000Z
DTEND:20200630T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/9
DESCRIPTION:Title: Symplectic mapping class groups and homological mirror symmetry\nby N
ick Sheridan (Edinburgh) as part of Free Mathematics Seminar\n\n\nAbstract
\nI will explain how one can get new information about symplectic mapping
class groups by combining two recent results: a proof of homological mirro
r symmetry for a new collection of K3 surfaces (joint work with Ivan Smith
)\, together with the computation of the derived autoequivalence group of
a K3 surface of Picard rank one (Bayer--Bridgeland). For example\, it is p
ossible to give an example of a symplectic K3 whose smoothly trivial sympl
ectic mapping class group (the group of isotopy classes of symplectic auto
morphisms which are smoothly isotopic to the identity) is infinitely-gener
ated. This is joint work with Ivan Smith.\n
LOCATION:https://researchseminars.org/talk/Freemath/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammed Abouzaid (Columbia)
DTSTART:20200707T140000Z
DTEND:20200707T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/10
DESCRIPTION:Title: Floer homotopy without spectra\nby Mohammed Abouzaid (Columbia) as p
art of Free Mathematics Seminar\n\n\nAbstract\nThe construction of Cohen-J
ones-Segal of Floer homotopy types associated to appropriately oriented fl
ow categories extracts from the morphisms of such a category the data requ
ired to assemble an iterated extension of free modules (in an appropriate
category of spectra). I will explain a direct (geometric) way for defining
the Floer homotopy groups which completely bypasses stable homotopy theor
y. The key point is to work on the geometric topology side of the Pontryag
in-Thom construction. Time permitting\, I will also explain joint work in
progress with Blumberg for building a spectrum from the new point of view\
, as well as various generalisations which are relevant to Floer theory.\n
LOCATION:https://researchseminars.org/talk/Freemath/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheel Ganatra
DTSTART:20200714T140000Z
DTEND:20200714T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/11
DESCRIPTION:Title: On Rabinowitz wrapped Fukaya categories\nby Sheel Ganatra as part of
Free Mathematics Seminar\n\n\nAbstract\nThis talk develops the open-strin
g categorical analogue of Rabinowitz Floer homology\, which we term the Ra
binowitz (wrapped) Fukaya category. Following a conjecture of Abouzaid\,
we relate the Rabinowitz Fukaya category to the usual wrapped Fukaya categ
ory by way of a general categorical construction introduced by Efimov\, th
e "categorical formal punctured neighborhood of infinity". Using this res
ult\, we show how Rabinowitz Fukaya categories can be fit into - and there
fore computed in terms of - mirror symmetry. Joint work (in progress) wit
h Yuan Gao and Sara Venkatesh.\n
LOCATION:https://researchseminars.org/talk/Freemath/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Craw
DTSTART:20200721T140000Z
DTEND:20200721T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/12
DESCRIPTION:Title: Hilbert schemes of ADE singularities as quiver varieties\nby Alastai
r Craw as part of Free Mathematics Seminar\n\n\nAbstract\nThe nth symmetri
c product of a ADE surface singularity is well known to be a Nakajima quiv
er variety. I will describe recent work with Gammelgaard\, Gyenge and Szen
droi in which the Hilbert scheme of n points on the ADE singularity is con
structed as a Nakajima quiver variety. This result provided the catalyst f
or the description of the generating function of Euler numbers on punctual
Hilbert schemes of an ADE surface singularity by Nakajima earlier this ye
ar.\n
LOCATION:https://researchseminars.org/talk/Freemath/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Cannizzo
DTSTART:20200728T140000Z
DTEND:20200728T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/13
DESCRIPTION:Title: Towards global homological mirror symmetry for genus 2 curves\nby Ca
therine Cannizzo as part of Free Mathematics Seminar\n\n\nAbstract\nThe fi
rst part of the talk will discuss work in https://arxiv.org/abs/1908.04227
on constructing a Donaldson-Fukaya-Seidel type category for the generaliz
ed SYZ mirror of a genus 2 curve. We will explain the categorical mirror c
orrespondence on the cohomological level. The key idea uses that a 4-torus
is SYZ mirror to a 4-torus. So if we view the complex genus 2 curve as a
hypersurface of a 4-torus V\, a mirror can be constructed as a symplectic
fibration with fiber given by the dual 4-torus V^. Hence on categories\, l
ine bundles on V are restricted to the genus 2 curve while fiber Lagrangia
ns of V^ are parallel transported over U-shapes in the base of the mirror.
Next we describe ongoing work with H. Azam\, H. Lee\, and C-C. M. Liu on
extending the result to a global statement\, namely allowing the complex a
nd symplectic structures to vary in their real six-dimensional families. T
he mirror statement for this more general result relies on work of A. Kana
zawa and S-C. Lau.\n
LOCATION:https://researchseminars.org/talk/Freemath/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Kartal
DTSTART:20200804T140000Z
DTEND:20200804T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/14
DESCRIPTION:Title: p-adic analytic actions on the Fukaya category and iterates of symplect
omorphisms\nby Baris Kartal as part of Free Mathematics Seminar\n\n\nA
bstract\nA theorem of J. Bell states that given a complex affine \nvariety
$X$ with an automorphism $\\phi$\, and a subvariety $Y\\subset \nX$\, the
set of numbers $k$ such that $\\phi^k(x)\\in Y$ is a union of \nfinitely
many arithmetic progressions and finitely many numbers. \nMotivated by thi
s statement\, Seidel asked whether there is a \nsymplectic analogue of thi
s theorem. In this talk\, we give an answer \nto a version of this questio
n in the case $M$ is monotone\, \nnon-degenerate and $\\phi$ is symplectic
ally isotopic to identity. The \nmain tool is analogous to the main tool i
n Bell's proof: namely we \ninterpolate the powers of $\\phi$ by a p-adic
arc\, constructing an \nanalytic action of $\\mathbb{Z}_p$ on the Fukaya c
ategory.\n
LOCATION:https://researchseminars.org/talk/Freemath/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dougal Davis
DTSTART:20200811T090000Z
DTEND:20200811T100000Z
DTSTAMP:20260422T225755Z
UID:Freemath/15
DESCRIPTION:Title: Surface singularities and their deformations via principal bundles on el
liptic curves\nby Dougal Davis as part of Free Mathematics Seminar\n\n
\nAbstract\nIt is well known that du Val (aka simple\, Kleinian\, ADE\, ..
.) singularities of algebraic surfaces are classified by Dynkin diagrams o
f type ADE. A geometric link between the singularity and the Lie algebra o
f the same type was given by Brieskorn in the 70s\, who showed that the si
ngularity can be recovered by intersecting the nilpotent cone inside the L
ie algebra with a transversal slice through a subregular nilpotent element
. Brieskorn's construction also realises the entire transversal slice as t
he total space of a miniversal deformation of the singularity. In this tal
k\, I will discuss an elliptic version of this story\, where the Lie algeb
ra is replaced with the stack of principal bundles on an elliptic curve. T
here is still a notion of subregular slice in this stack\, and one gets a
singular surface by intersecting such a thing with the locus of unstable b
undles. I will explain which surfaces arise in this way\, and in what sens
e the subregular slice is still the total space of a miniversal deformatio
n. Time permitting\, I will also touch on how the BCFG types are related t
o the ADE ones (in a different way to the story for Lie algebras!)\, and o
n some questions about Poisson structures and their quantisations.\n
LOCATION:https://researchseminars.org/talk/Freemath/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giancarlo Urzúa
DTSTART:20200820T140000Z
DTEND:20200820T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/16
DESCRIPTION:Title: On the geography of complex surfaces of general type with an arbitrary f
undamental group\nby Giancarlo Urzúa as part of Free Mathematics Semi
nar\n\n\nAbstract\nSurfaces of general type are lovely unclassifiable obje
cts in algebraic geometry. Geography refers to the problem of construction
of such surfaces for a given set of invariants\, classically the Chern nu
mbers \\(c_1^2\\) (self-intersection of canonical class) and \\(c_2\\) (to
pological Euler characteristic). In this talk\, we treat the question: Wha
t can be said about the distribution of Chern slopes \\(c_1^2/c_2\\) of su
rfaces of general type when we fix the fundamental group? It turns out tha
t there are various well-known constraints\, which will be pointed out dur
ing the talk\, but at least we can prove the following theorem (joint with
Sergio Troncoso): "Let \\(G\\) be the fundamental group of some nonsingul
ar complex projective variety. Then Chern slopes of surfaces of general t
ype with fundamental group isomorphic to \\(G\\) are dense in the interval
\\([1\,3]\\).". Remember that for complex surfaces of general type we hav
e that \\(c_1^2/c_2\\) is a rational number in \\([1/5\,3]\\)\, and so mos
t open questions now refer to slopes in \\([1/5\,1]\\). On the other hand\
, it is known that every finite group is the fundamental group of some non
singular projective variety\, and so a lot is going on for high slopes.\n
LOCATION:https://researchseminars.org/talk/Freemath/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inbar Klang
DTSTART:20200825T140000Z
DTEND:20200825T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/17
DESCRIPTION:Title: Twisted Calabi-Yau algebras and categories\nby Inbar Klang as part o
f Free Mathematics Seminar\n\n\nAbstract\nThis talk will begin with a disc
ussion of the string topology category of a manifold $M$\; this was shown
by Cohen and Ganatra to be equivalent as a Calabi-Yau category to the wrap
ped Fukaya category of $T^*M$. In joint work with Ralph Cohen\, we general
ize the Calabi-Yau condition from chain complexes to spectra. I'll talk ab
out these Calabi-Yau ring spectra and discuss examples of interest.\n
LOCATION:https://researchseminars.org/talk/Freemath/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wai Kit Yeung
DTSTART:20200901T140000Z
DTEND:20200901T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/18
DESCRIPTION:Title: Pre-Calabi-Yau categories\nby Wai Kit Yeung as part of Free Mathemat
ics Seminar\n\n\nAbstract\nPre-Calabi-Yau categories are algebraic structu
res first studied by Kontsevich and Vlassopoulos. They can be viewed as a
noncommutative analogue of Poisson structures\, just like Calabi-Yau struc
tures are a noncommutative analogue of symplectic structures. It is expect
ed that disk-counting with more than one output endows Fukaya categories w
ith pre-Calabi-Yau structures. In this talk\, we discuss several aspects o
f this notion.\n
LOCATION:https://researchseminars.org/talk/Freemath/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Macpherson
DTSTART:20200908T090000Z
DTEND:20200908T100000Z
DTSTAMP:20260422T225755Z
UID:Freemath/19
DESCRIPTION:Title: A bivariant Yoneda lemma and (infinity\, 2)-categories of correspondence
s\nby Andrew Macpherson as part of Free Mathematics Seminar\n\n\nAbstr
act\nThe notion of the *category of correspondences* of a category D with
a specified\, base change stable\, class of morphisms S --- whose objects
are those of D and whose morphisms are "spans" in D\, one side of which be
longs to S --- will be familiar to practitioners of Grothendieck's theory
of motives. Perhaps less familiar is the fact that an obvious 2-categorica
l upgrade of correspondences has a universal property: it is the universal
way to attach right adjoints to members of S subject to a base change for
mula.\n\nI will explain a little about the state of the art on enriched an
d iterated higher categories and show that they can be used to provide a c
onceptual (that is\, no explicit homotopy- or simplex-chasing) proof of th
is phenomenon for (infinity\, 2)-categories. This enhancement opens the do
or to direct constructions of bivariant homology theories in motivic homot
opy theory and beyond.\n
LOCATION:https://researchseminars.org/talk/Freemath/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Golla
DTSTART:20200915T140000Z
DTEND:20200915T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/20
DESCRIPTION:Title: Symplectic hats\nby Marco Golla as part of Free Mathematics Seminar\
n\n\nAbstract\nA hat for a transverse knot in a symplectic cap of a contac
t 3-manifold is a symplectic surface in the cap whose boundary is the knot
. I will talk about existence\, obstructions\, and properties of hats\, wi
th an emphasis on the standard 3-sphere\, and about an application to Stei
n fillings. This is joint work with John Etnyre.\n
LOCATION:https://researchseminars.org/talk/Freemath/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Gayet
DTSTART:20200922T140000Z
DTEND:20200922T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/21
DESCRIPTION:Title: Lagrangians of (random) projective hypersurfaces\nby Damien Gayet as
part of Free Mathematics Seminar\n\n\nAbstract\nI will explain that any s
mooth compact hypersurface in $\\mathbb R^n$ appears (up to diffeomorphism
) a very large number of times as disjoint Lagrangians in any complex hype
rsurface of $\\mathbb C P^n$\, if the degree of the hypersurface is high e
nough. Suprisingly\, the proof holds on probabilistic arguments.\n
LOCATION:https://researchseminars.org/talk/Freemath/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Manion
DTSTART:20201020T140000Z
DTEND:20201020T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/23
DESCRIPTION:Title: Higher representations and cornered Floer homology\nby Andrew Manion
as part of Free Mathematics Seminar\n\n\nAbstract\nI will discuss recent
work with Raphael Rouquier\, focusing on a higher tensor product operation
for 2-representations of Khovanov's categorification of U(gl(1|1)^+)\, ex
amples of such 2-representations that arise as strands algebras in bordere
d and cornered Heegaard Floer homology\, and a tensor-product-based gluing
formula for these 2-representations expanding on work of Douglas-Manolesc
u.\n
LOCATION:https://researchseminars.org/talk/Freemath/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francois Greer
DTSTART:20201027T150000Z
DTEND:20201027T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/24
DESCRIPTION:Title: Cycle-valued quasi-modular forms on Kontsevich space\nby Francois Gr
eer as part of Free Mathematics Seminar\n\n\nAbstract\nOn a general ration
al elliptic surface (fibered over $\\mathbb{P}^1$)\, the number of section
s of height $n$ is equal to the coefficient of the Eisenstein series $E_4(
q)$ at order $n+1$. I will describe a conjectural generalization of this f
act\, which associates to any smooth projective variety a quasi-modular fo
rm valued in the Chow group of its Kontsevich moduli space. The proof is i
n progress.\n
LOCATION:https://researchseminars.org/talk/Freemath/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Belmans
DTSTART:20201006T140000Z
DTEND:20201006T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/25
DESCRIPTION:Title: Graph potentials as mirrors to moduli of vector bundles on curves\nb
y Pieter Belmans as part of Free Mathematics Seminar\n\n\nAbstract\nIn a j
oint work with Sergey Galkin and Swarnava Mukhopadhyay we have a class of
Laurent polynomials associated to decorated trivalent graphs which we call
ed graph potentials. These Laurent polynomials satisfy interesting symmetr
y and compatibility properties. Under mirror symmetry they are related to
moduli spaces of rank 2 bundles (with fixed determinant of odd degree) on
a curve of genus $g\\geq 2$\, which is a class of Fano varieties of dimens
ion $3g-3$. I will discuss (parts of) the (enumerative / homological) mirr
or symmetry picture for Fano varieties\, and then explain what we understa
nd for this class of varieties and what we can say about the (conjectural)
semiorthogonal decomposition of the derived category.\n
LOCATION:https://researchseminars.org/talk/Freemath/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenji Fukaya
DTSTART:20201208T150000Z
DTEND:20201208T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/26
DESCRIPTION:Title: Atiyah-Floer type conjecture and Virtual fundamental chain\nby Kenji
Fukaya as part of Free Mathematics Seminar\n\n\nAbstract\nThis is a repor
t on my work in progress with Aliakbar Daemi\n\nWe are studying an SO(3) v
ersion of Atiyah-Floer conjecture relating Instanton Floer homology to Lag
rangian Floer homology\, via cobordism method. In the case when the moduli
space of flat connections on 3 manifold is an {\\it embedded} Lagrangian
submanifold of the space of flat connections on 2 manifold\, we can pertur
b Lipyanskiy type mixed moduli space using geometric perturbation. In the
case it is an immersed Lagrangian submanifold\, we need abstract perturbat
ion and virtual technique. The singularity of the instanton moduli space i
s wilder than the case of pseudo-holomorphic curve and we need certain `st
ratified' version of Kuranishi structure. I will explain how we can define
such a notion\, show the existence of such structure and use it to obtain
virtual fundamental chain.\n
LOCATION:https://researchseminars.org/talk/Freemath/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hansol Hong
DTSTART:20201013T090000Z
DTEND:20201013T100000Z
DTSTAMP:20260422T225755Z
UID:Freemath/27
DESCRIPTION:Title: Maurer-Cartan deformation of a Lagrangian\nby Hansol Hong as part of
Free Mathematics Seminar\n\n\nAbstract\nThe Maurer-Cartan algebra of a La
grangian is the algebra that encodes the deformation of its Floer complex
as an A-infinity algebra. I will give a convenient description of the Maur
er-Cartan algebra through a natural homological algebra language\, and rel
ate it with (a version of) Koszul duality for the Floer complex. It helps
us to obtain the mirror-symmetry interpretation for the Maurer-Cartan defo
rmation and its locality in SYZ situation. Namely\, the Maurer-Cartan alge
bra provides a neighborhood of the point mirror to the Lagrangian\, which
varies in size depending on geometric types of Floer generators involved i
n the deformation.\n
LOCATION:https://researchseminars.org/talk/Freemath/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Bridgeland
DTSTART:20201110T150000Z
DTEND:20201110T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/28
DESCRIPTION:Title: Donaldson-Thomas invariants and a non-perturbative topological string pa
rtition function\nby Tom Bridgeland as part of Free Mathematics Semina
r\n\n\nAbstract\nI will introduce a class of Riemann-Hilbert problems whic
h (I claim) arise naturally in Donaldson-Thomas theory. I will start with
the simplest example (corresponding to the DT theory of the A1 quiver) whi
ch leads via undergraduate mathematics to the gamma function. Then I will
explain how the same procedure applied to the DT theory of coherent sheave
s on the resolved conifold leads to a non-perturbative version of the Grom
ov-Witten generating series\, i.e. a particular choice of holomorphic func
tion having this series as its asymptotic expansion (in fact the same resu
lt holds for any non-compact CY threefold having no compact divisors). If
there is time left at the end (which there never is) I will discuss recent
attempts to go beyond these results.\n
LOCATION:https://researchseminars.org/talk/Freemath/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Côté
DTSTART:20201103T150000Z
DTEND:20201103T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/29
DESCRIPTION:Title: Homological invariants of codimension 2 contact embeddings\nby Laure
nt Côté as part of Free Mathematics Seminar\n\n\nAbstract\nThere is a ri
ch theory of transverse knots in 3-dimensional contact manifolds. It was a
major open question in contact topology whether non-trivial transverse kn
ots (i.e. codimension 2 contact embeddings) also exist in higher dimension
s. This question was recently settled in the affirmative by Casals and Etn
yre. Motivated by their result\, I will talk about recent work with Franco
is-Simon Fauteux-Chapleau in which we develop invariants of codimension 2
contact embeddings using the machinery of symplectic field theory.\n
LOCATION:https://researchseminars.org/talk/Freemath/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyler Siegel
DTSTART:20201117T150000Z
DTEND:20201117T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/30
DESCRIPTION:Title: On the embedding complexity of Liouville manifolds\nby Kyler Siegel
as part of Free Mathematics Seminar\n\n\nAbstract\nI will describe a new f
ramework for obstructing exact symplectic embeddings between Liouville man
ifolds\, based on L-infinity structures in symplectic field theory. As a m
ain application\, we study embeddings between normal crossing divisor comp
lements in complex projective space\, giving a complete characterization i
n many cases. This is based on joint work in preparation with S. Ganatra.\
n
LOCATION:https://researchseminars.org/talk/Freemath/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Mclean
DTSTART:20201124T150000Z
DTEND:20201124T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/31
DESCRIPTION:Title: Floer Cohomology and Arc Spaces\nby Mark Mclean as part of Free Math
ematics Seminar\n\n\nAbstract\nLet f be a polynomial over the complex numb
ers with an isolated singular point at the origin and let d be a positive
integer. To such a polynomial we can assign a variety called the dth conta
ct locus of f. Morally\, this corresponds to the space of d-jets of holomo
rphic disks in complex affine space whose boundary `wraps' around the sing
ularity d times. We show that Floer cohomology of the dth power of the Mil
nor monodromy map is isomorphic to compactly supported cohomology of the d
th contact locus. This answers a question of Paul Seidel and it also prove
s a conjecture of Nero Budur\, Javier Fernández de Bobadilla\, Quy Thuo
ng Lê and Hong Duc Nguyen. The key idea of the proof is to use a jet sp
ace version of the PSS map together with a filtration argument.\n
LOCATION:https://researchseminars.org/talk/Freemath/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Lin
DTSTART:20201201T150000Z
DTEND:20201201T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/32
DESCRIPTION:Title: Floer homology and closed geodesics of hyperbolic three-manifolds\nb
y Francesco Lin as part of Free Mathematics Seminar\n\n\nAbstract\nFloer h
omology and hyperbolic geometry are fundamental tools in the study of thre
e-dimensional topology. Despite this\, it remains an outstanding problem t
o understand whether there is any relationship between them. I will discus
s some results in this direction that use as stepping stone the spectral g
eometry of coexact 1-forms. This is joint work with M. Lipnowski.\n
LOCATION:https://researchseminars.org/talk/Freemath/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Álvarez-Gavela
DTSTART:20201215T150000Z
DTEND:20201215T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/33
DESCRIPTION:Title: Polarized Weinstein manifolds and their positive arboreal skeleta\nb
y Daniel Álvarez-Gavela as part of Free Mathematics Seminar\n\n\nAbstract
\nThe goal of this talk is to give a geometric introduction to arboreal si
ngularities\, as well as to the distinguished subclass of *positive* arbor
eal singularities\, and to state precisely the theorem joint with Y. Elias
hberg and D. Nadler that a Weinstein manifold admits a global field of Lag
rangian planes if and only if the Weinstein structure can be deformed so t
hat the skeleton becomes positive arboreal. In particular it follows that
complete intersections in complex affine space can be arborealized.\n
LOCATION:https://researchseminars.org/talk/Freemath/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner
DTSTART:20210112T150000Z
DTEND:20210112T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/34
DESCRIPTION:Title: Derived Theta-stratifications and the D-equivalence conjecture\nby D
aniel Halpern-Leistner as part of Free Mathematics Seminar\n\n\nAbstract\n
Every vector bundle on a smooth curve has a canonical filtration\, called
the Harder-Narasimhan filtration\, and the moduli of all vector bundles ad
mits a stratification based on the properties of the Harder-Narasimhan fil
tration at each point. The theory of Theta-stratifications formulates this
structure on a general algebraic stack. I will discuss how to characteriz
e stratifications of this kind\, and why their local cohomology is particu
larly well-behaved. I will then explain how Theta-stratifications are part
of a recent proof of a case of the D-equivalence conjecture: for any proj
ective Calabi-Yau manifold X that is birationally equivalent to a moduli s
pace of semistable coherent sheaves on a K3 surface\, the derived category
of coherent sheaves on X is equivalent to the derived category of this mo
duli space. This confirms a prediction from homological mirror symmetry fo
r this class of compact Calabi-Yau manifold\n
LOCATION:https://researchseminars.org/talk/Freemath/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvain Courte
DTSTART:20210119T150000Z
DTEND:20210119T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/35
DESCRIPTION:Title: Twisted generating functions and the nearby Lagrangian conjecture\nb
y Sylvain Courte as part of Free Mathematics Seminar\n\n\nAbstract\nI will
explain the notion of twisted generating function and show that a closed
exact Lagrangian submanifold L in the cotangent bundle of M admits such a
thing. The type of function arising in our construction is related to Wald
hausen's tube space from his manifold approach to algebraic K-theory of sp
aces. Using the rational equivalence of this space with BO\, as proved by
Bökstedt\, we conclude that the stable Lagrangian Gauss map of L vanishes
on all homotopy groups. In particular when M is a homotopy sphere\, we ob
tain the triviality of the stable Lagrangian Gauss map and a genuine gener
ating function for L. This is a joint work with M. Abouzaid\, S. Guillermo
u and T. Kragh.\n
LOCATION:https://researchseminars.org/talk/Freemath/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Gammage
DTSTART:20210126T150000Z
DTEND:20210126T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/36
DESCRIPTION:Title: Mirror symmetry for Berglund-Hübsch Milnor fibers\nby Benjamin Gamm
age as part of Free Mathematics Seminar\n\n\nAbstract\nAfter recalling som
e joint work with Jack Smith proving homological Berglund-Hübsch mirror s
ymmetry\, we explain the calculation of the Fukaya category of a Berglund-
Hübsch Milnor fiber\, proving a conjecture of Yankı Lekili and Kazushi U
eda\; the main technical trick is the reduction of the calculation to a ce
rtain extension of perverse schobers\, essentially already computed by Dav
id Nadler.\n
LOCATION:https://researchseminars.org/talk/Freemath/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Jeffs
DTSTART:20210202T150000Z
DTEND:20210202T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/37
DESCRIPTION:Title: Mirror symmetry and Fukaya categories of singular varieties\nby Maxi
m Jeffs as part of Free Mathematics Seminar\n\n\nAbstract\nIn this talk I
will explain Auroux' definition of the Fukaya category of a singular hyper
surface and two results about this definition\, illustrated with some exam
ples. The first result is that Auroux' category is equivalent to the Fukay
a-Seidel category of a Landau-Ginzburg model on a smooth variety\; the sec
ond result is a homological mirror symmetry equivalence at certain large c
omplex structure limits. I will also discuss ongoing work on generalizatio
ns.\n
LOCATION:https://researchseminars.org/talk/Freemath/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junwu Tu
DTSTART:20210209T150000Z
DTEND:20210209T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/38
DESCRIPTION:Title: On the categorical enumerative invariants of a point\nby Junwu Tu as
part of Free Mathematics Seminar\n\n\nAbstract\nWe briefly recall the def
inition of categorical enumerative invariants (CEI) first introduced by Co
stello around 2005. Costello's construction relies fundamentally on Sen-Zw
iebach's notion of string vertices V_{g\,n}'s which are chains on moduli s
pace of smooth curves M_{g\,n}'s. In this talk\, we explain the relationsh
ip between string vertices and the fundamental classes of the Deligne-Mumf
ord compactification of M_{g\,n}. More precisely\, we obtain a Feynman sum
formula expressing the fundamental classes in terms of string vertices. A
s an immediate application\, we prove a comparison result that the CEI of
the field \\mathbb{Q} is the same as the Gromov-Witten invariants of a poi
nt.\n
LOCATION:https://researchseminars.org/talk/Freemath/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Habermann
DTSTART:20210216T150000Z
DTEND:20210216T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/39
DESCRIPTION:Title: Homological mirror symmetry for nodal stacky curves\nby Matthew Habe
rmann as part of Free Mathematics Seminar\n\n\nAbstract\nIn this talk I wi
ll explain the proof of homological mirror symmetry where the B-side is a
ring or chain of stacky projective lines joined nodally\, and where each i
rreducible component is allowed to have a non-trivial generic stabiliser\,
generalising the work of Lekili and Polishchuk. The key ingredient is to
match categorical resolutions on the A- and B-sides with an intermediary c
ategory given by the derived category of modules of a gentle algebra. I wi
ll begin by explaining how to construct this category from the data of the
A- and B-models before moving on to applications. In particular\, one can
show homological mirror symmetry where the B-model is taken to be an inve
rtible polynomial in two variables\, but where the grading group is not ne
cessarily maximal. In the maximally graded case the mirror is shown to be
graded symplectomorphic to the Milnor fibre of the transpose invertible po
lynomial\, thus establishing the Lekili-Ueda conjecture in dimension one.\
n
LOCATION:https://researchseminars.org/talk/Freemath/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Doan
DTSTART:20210223T140000Z
DTEND:20210223T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/40
DESCRIPTION:Title: Counting pseudo-holomorphic curves in symplectic six-manifolds\nby A
leksander Doan as part of Free Mathematics Seminar\n\n\nAbstract\nThe sign
ed count of embedded pseudo-holomorphic curves in a symplectic manifold ty
pically depends on the choice of an almost complex structure on the manifo
ld and so does not lead to a symplectic invariant. However\, I will discus
s two instances in which such naive counting does define a symplectic inva
riant. The proof of invariance combines methods of symplectic geometry wit
h results of geometric measure theory\, especially regularity theory for c
alibrated currents. The talk is based on joint work with Thomas Walpuski.
Time permitting\, I will also discuss a related project\, joint with Eleny
Ionel and Thomas Walpuski\, whose goal is to use geometric measure theory
to prove the Gopakumar-Vafa finiteness conjecture.\n
LOCATION:https://researchseminars.org/talk/Freemath/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Wilkins
DTSTART:20210302T150000Z
DTEND:20210302T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/41
DESCRIPTION:Title: Quantum Steenrod operations are covariant constant\nby Nicholas Wilk
ins as part of Free Mathematics Seminar\n\n\nAbstract\nWe explore the quan
tum Steenrod operations (which are quantum cohomology operations that util
ise a symmetry under the cyclic group of order p)\, and observe that these
operations are covariant constant with respect to the quantum connection.
In particular\, they can be partially calculated in a variety of cases (a
nd fully calculated in a subset). This work is joint with Paul Seidel.\n
LOCATION:https://researchseminars.org/talk/Freemath/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Shelukhin
DTSTART:20210316T150000Z
DTEND:20210316T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/42
DESCRIPTION:Title: Lagrangian configurations and Hamiltonian maps\nby Egor Shelukhin as
part of Free Mathematics Seminar\n\n\nAbstract\nWe study configurations o
f disjoint Lagrangian submanifolds in certain low-dimensional symplectic m
anifolds from the perspective of the geometry of Hamiltonian maps. We dete
ct infinite-dimensional flats in the Hamiltonian group of the two-sphere e
quipped with Hofer's metric\, showing in particular that this group is not
quasi-isometric to a line. This answers a well-known question of Kapovich
-Polterovich from 2006. We show that these flats in Ham(S^2) stabilize to
certain product four-manifolds\, prove constraints on Lagrangian packing\
, find new instances of Lagrangian Poincare recurrence\, and present a new
hierarchy of normal subgroups of area-preserving homeomorphisms of the tw
o-sphere. The technology involves Lagrangian spectral invariants with Hami
ltonian term in symmetric product orbifolds. This is joint work with Leoni
d Polterovich.\n
LOCATION:https://researchseminars.org/talk/Freemath/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abigail Ward
DTSTART:20210309T150000Z
DTEND:20210309T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/43
DESCRIPTION:Title: Mirror symmetry for certain non-Kähler elliptic surfaces\nby Abigai
l Ward as part of Free Mathematics Seminar\n\n\nAbstract\nThe logarithmic
transformation is an operation on complex elliptic surfaces which can be u
sed to produce interesting spaces from more familiar ones. I will first gi
ve homological mirror symmetry results for surfaces which are constructed
by performing two logarithmic transformations to the product of P^1 with a
n elliptic curve\, a class of surfaces which includes the classical Hopf s
urface (S^1 x S^3). I will then use this work\, along with work of Auroux\
, Efimov and Katzarkov on the Fukaya category of singular curves\, to desc
ribe some work in progress on a potential mirror operation to the logarith
mic transformation and some applications.\n
LOCATION:https://researchseminars.org/talk/Freemath/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Kirchhoff-Lukat
DTSTART:20210323T150000Z
DTEND:20210323T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/44
DESCRIPTION:Title: Towards Floer theory and Fukaya categories for Generalized Complex Manif
olds: Some first ideas\nby Charlotte Kirchhoff-Lukat as part of Free M
athematics Seminar\n\n\nAbstract\nGeneralized complex (GC) manifolds encom
pass both symplectic and complex manifolds as examples. From the inception
of the field of GC geometry in the early 2000s\, questions have thus been
raised about its relation to mirror symmetry: Can mirror symmetry be unde
rstood as a generalized complex duality\, and if so\, how? An answer to th
is general question currently seems out of reach both from the point of vi
ew of mirror symmetry\, as well as GC geometry -- general GC manifolds are
so far relatively poorly understood. However\, I have identified a number
specific initial questions and approaches which I hope will ultimately he
lp a more general understanding. These ideas -- currently still in their i
nfancy -- are what I would like to outline in this talk.\n
LOCATION:https://researchseminars.org/talk/Freemath/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conan Leung
DTSTART:20210330T140000Z
DTEND:20210330T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/45
DESCRIPTION:Title: Quantum cohomology of flag varieties via wonderful compactifications
\nby Conan Leung as part of Free Mathematics Seminar\n\n\nAbstract\nPeters
on conjectured that quantum cohomlogy ring of G/T is isomorphic to the hom
ology of the based loop space of G after localization. Lam and Shimozono p
roved the conjecture by combinatorial method. We studied the wrapped Floer
theory of the complexification of G and used the geometry of its wonderfu
l compactification to give a geometric proof of this result.\n
LOCATION:https://researchseminars.org/talk/Freemath/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Le
DTSTART:20210413T090000Z
DTEND:20210413T100000Z
DTSTAMP:20260422T225755Z
UID:Freemath/46
DESCRIPTION:Title: Mirror Symmetry for Truncated Cluster Varieties\nby Ian Le as part o
f Free Mathematics Seminar\n\n\nAbstract\nGross\, Hacking and Keel gave an
algebro-geometric construction of cluster varieties: take a toric variety
\, blow up appropriate subvarieties in the boundary\, and then remove the
strict transform of the boundary. We work with a modification of this cons
truction\, which we call a truncated cluster variety--roughly\, this comes
from performing the same procedure on the toric variety with all the codi
mension 2 strata removed. The resulting variety differs from the cluster v
ariety in codimension 2. I will describe a construction of a Weinstein man
ifold mirror to a truncated cluster variety and explain how to prove a mir
ror symmetry via Lagrangian skeleta. We hope that this is a first step tow
ards understanding mirror symmetry for the entire cluster variety. This is
joint work with Benjamin Gammage.\n
LOCATION:https://researchseminars.org/talk/Freemath/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Pomerleano
DTSTART:20210420T140000Z
DTEND:20210420T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/47
DESCRIPTION:Title: Intrinsic Mirror Symmetry and Categorical Crepant Resolutions\nby Da
n Pomerleano as part of Free Mathematics Seminar\n\n\nAbstract\nA general
expectation in mirror symmetry is that the mirror partner to an affine log
Calabi-Yau variety is "semi-affine" (meaning it is proper over its affini
zation). We will discuss how the semi-affineness of the mirror can be seen
directly as certain finiteness properties of Floer theoretic invariants o
f X (the symplectic cohomology and wrapped Fukaya category). One interesti
ng consequence of these finiteness results is that\, under fairly general
circumstances\, the wrapped Fukaya of X gives an ("intrinsic") categorical
crepant resolution of the affine variety Spec(SH^0(X)). This is based on
https://arxiv.org/pdf/2103.01200.pdf.\n
LOCATION:https://researchseminars.org/talk/Freemath/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolo Sibilla
DTSTART:20210427T140000Z
DTEND:20210427T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/48
DESCRIPTION:Title: Fukaya category of surfaces and pants decomposition\nby Nicolo Sibil
la as part of Free Mathematics Seminar\n\n\nAbstract\nIn this talk I will
explain some results joint with James Pascaleff on the Fukaya category of
Riemann surfaces. I will explain a local-to-global principle which allows
us to reduce the calculation of the Fukaya category of surfaces of genus g
greater than one to the case of the pair-of-pants\, and which holds both
in the punctured and in the compact case. The starting point are the sheaf
-theoretic methods which are available in the exact setting\, and which I
will review at the beginning of the talk. This result has several interest
ing consequences for HMS and geometrization of objects in the Fukaya categ
ory. The talk is based on 1604.06448 and 2103.03366.\n
LOCATION:https://researchseminars.org/talk/Freemath/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Rana
DTSTART:20210504T140000Z
DTEND:20210504T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/49
DESCRIPTION:Title: T-singular surfaces of general type\nby Julie Rana as part of Free M
athematics Seminar\n\n\nAbstract\nWe explore the moduli space of stable su
rfaces\, where the simplest of questions continue to remain open for almos
t all invariants. A few such questions: Of the allowable singularities\, w
hich ones actually occur on a stable surface? Which of these deform to smo
oth surfaces? How can we use this knowledge to find divisors in the moduli
spaces? Can we develop a stratification of these moduli spaces by singula
rity type? Our focus will be on cyclic quotient singularities\, with an em
phasis on discussing concrete visual examples built out of rational\, K3\,
and elliptic surfaces.\n
LOCATION:https://researchseminars.org/talk/Freemath/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yin Li
DTSTART:20210511T140000Z
DTEND:20210511T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/50
DESCRIPTION:Title: Exact Lagrangian tori in affine varieties\nby Yin Li as part of Free
Mathematics Seminar\n\n\nAbstract\nWe will discuss what is known and unkn
own about the existence of exact Lagrangian tori in smooth affine varietie
s. Based on homological mirror symmetry and computations of Hochschild coh
omology\, we prove the nonexistence of exact Lagrangian tori in a class of
affine conic bundles over C^n\, which cannot in general be embedded in th
e complement of ample divisors in smooth Fano varieties. This result shoul
d be regarded as evidence for the existence of dilations.\n
LOCATION:https://researchseminars.org/talk/Freemath/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Sertöz
DTSTART:20210518T140000Z
DTEND:20210518T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/51
DESCRIPTION:Title: Separating periods of quartic surfaces\nby Emre Sertöz as part of F
ree Mathematics Seminar\n\n\nAbstract\nKontsevich--Zagier periods form a n
atural number system that extends the algebraic numbers by adding constant
s coming from geometry and physics. Because there are countably many perio
ds\, one would expect it to be possible to compute effectively in this num
ber system. This would require an effective height function and the abilit
y to separate periods of bounded height\, neither of which are currently p
ossible.\n\nIn this talk\, we introduce an effective height function for p
eriods of quartic surfaces defined over algebraic numbers. We also determi
ne the minimal distance between periods of bounded height on a single surf
ace. We use these results to prove heuristic computations of Picard groups
that rely on approximations of periods. Moreover\, we give explicit Liouv
ille type numbers that can not be the ratio of two periods of a quartic su
rface. This is joint work with Pierre Lairez (Inria\, France).\n
LOCATION:https://researchseminars.org/talk/Freemath/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller
DTSTART:20210525T140000Z
DTEND:20210525T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/52
DESCRIPTION:Title: Singular Hochschild cohomology and reconstruction of singularities\n
by Bernhard Keller as part of Free Mathematics Seminar\n\n\nAbstract\nWe s
how that under a mild regularity assumption\, singular Hochschild cohomolo
gy (also known as Tate-Hochschild cohomology) identifies with Hochschild c
ohomology of the (dg enhanced) singularity category. In joint work with Zh
eng Hua\, we apply this to the reconstruction of a (complete isolated) com
pound Du Val singularity from its contraction algebra together with the ad
ditional datum of a class in its zeroth Hochschild homology. This provides
some evidence towards a conjecture by Donovan-Wemyss according to which t
he contraction algebra alone determines such a singularity.\n
LOCATION:https://researchseminars.org/talk/Freemath/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Hind
DTSTART:20210601T140000Z
DTEND:20210601T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/53
DESCRIPTION:Title: The shape invariant and path lifting\nby Richard Hind as part of Fre
e Mathematics Seminar\n\n\nAbstract\nThe shape invariant of a symplectic m
anifold encodes the area classes of Lagrangian submanifolds. This talk des
cribes joint work with Jun Zhang computing the shape for some simple domai
ns in 4-dimensional Euclidean space. We then consider the path lifting pro
blem\, which amounts to finding Lagrangian isotopies with specified flux.
Finally we discuss possible relations to stabilized symplectic embeddings.
\n
LOCATION:https://researchseminars.org/talk/Freemath/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Smith
DTSTART:20210608T140000Z
DTEND:20210608T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/54
DESCRIPTION:Title: Lagrangian links on surfaces and the Calabi invariant\nby Ivan Smith
as part of Free Mathematics Seminar\n\n\nAbstract\nThe identity component
in the group of area-preserving homeomorphisms of a compact surface admit
s a `mass-flow’ (or flux) homomorphism to the reals. We will prove that
the kernel of this homomorphism is not simple (extending earlier results
of Cristofaro-Gardiner\, Humilière and Seyfaddini in the genus zero case)
\, resolving a question of Fathi from the late 1970s. The proof appeals t
o a new family of Lagrangian spectral invariants associated to Lagrangian
links on the surface\, which are used to probe the small-scale geometry of
the surface\; their crucial feature is that they can be used to recover t
he classical Calabi invariant of a Hamiltonian. The Floer cohomology theo
ry behind these spectral invariants is a close cousin of the knot Floer ho
mology of Ozsváth-Szabó and Rasmussen. This talk reports on joint work
with Dan Cristofaro-Gardiner\, Vincent Humilière\, Cheuk Yu Mak and Sobha
n Seyfaddini.\n
LOCATION:https://researchseminars.org/talk/Freemath/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan Asplund
DTSTART:20210615T140000Z
DTEND:20210615T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/55
DESCRIPTION:Title: Chekanov-Eliashberg dg-algebras for singular Legendrians\nby Johan A
splund as part of Free Mathematics Seminar\n\n\nAbstract\nThe Chekanov-Eli
ashberg dg-algebra is a holomorphic curve invariant associated to a Legend
rian submanifold of a contact manifold. In this talk we explain how to ext
end the definition to singular Legendrian submanifolds admitting a Weinste
in neighborhood. Via the Bourgeois-Ekholm-Eliashberg surgery formula\, the
new definition gives direct geometric proof of the pushout diagrams and s
top removal formulas in partially wrapped Floer cohomology of Ganatra-Pard
on-Shende. It furthermore leads to a proof of the conjectured surgery form
ula relating partially wrapped Floer cohomology to Chekanov--Eliashberg dg
-algebras with coefficients in chains on the based loop space. This talk i
s based on joint work with Tobias Ekholm.\n
LOCATION:https://researchseminars.org/talk/Freemath/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Zemke
DTSTART:20210622T140000Z
DTEND:20210622T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/56
DESCRIPTION:Title: Heegaard Floer homology and complex curves with non-cuspidal singulariti
es\nby Ian Zemke as part of Free Mathematics Seminar\n\n\nAbstract\nWe
will discuss joint work with B. Liu and M. Borodzik\, concerning applicat
ions of Heegaard Floer d-invariants to the study of complex curves in $\\m
athbb{CP}^2$ with non-cuspidal singularities. We focus on the simplest suc
h singularity\, which is a double point.\n
LOCATION:https://researchseminars.org/talk/Freemath/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Jin
DTSTART:20210921T140000Z
DTEND:20210921T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/57
DESCRIPTION:Title: Homological mirror symmetry for the universal centralizers\nby Xin J
in as part of Free Mathematics Seminar\n\n\nAbstract\nI will present my re
cent result on homological mirror symmetry for the universal centralizer (
a.k.a Toda space) associated to a complex semisimple Lie group.\n The A
-side is a partially wrapped Fukaya category on the universal centralizer\
, and the B-side is the category of coherent sheaves on the categorical qu
otient of the dual maximal torus by the Weyl group (with some modification
s if the group has nontrivial center). I will illustrate many of the geome
try and ideas of the proof using the example of SL_2 or PGL_2.\n
LOCATION:https://researchseminars.org/talk/Freemath/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (University of Edinburgh)
DTSTART:20210928T140000Z
DTEND:20210928T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/58
DESCRIPTION:Title: Quantum cohomology as a deformation of symplectic cohomology\nby Umu
t Varolgunes (University of Edinburgh) as part of Free Mathematics Seminar
\n\n\nAbstract\nConsider a positively monotone closed symplectic manifold
$M$ and a symplectic simple crossings divisor $D$ in it. Assume that the P
oincare dual of the anti-canonical class is a positive rational linear com
bination of the classes $[D_i]$\, where $D_i$ are the components of $D$ wi
th their symplectic orientation. A choice of such coefficients\, called th
e weights\, (roughly speaking) equips $M-D$ with a Liouville structure. I
will start by discussing results relating the symplectic cohomology of $M-
D$ with quantum cohomology of $M$. These results are particularly sharp wh
en the weights are all at most 1 (hypothesis A). Then\, I will discuss cer
tain rigidity results (inside $M$) for skeleton type subsets of $M-D$\, wh
ich will also demonstrate the geometric meaning of hypothesis A in example
s. The talk will be mainly based on joint work with Strom Borman and Nick
Sheridan.\n
LOCATION:https://researchseminars.org/talk/Freemath/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Rains
DTSTART:20211019T160000Z
DTEND:20211019T170000Z
DTSTAMP:20260422T225755Z
UID:Freemath/59
DESCRIPTION:Title: The birational geometry of noncommutative surfaces\nby Eric Rains as
part of Free Mathematics Seminar\n\n\nAbstract\nIn commutative algebraic
geometry\, the theory of smooth projective surfaces is\, of course\, very
highly developed\, with a major result being the birational classification
of such surfaces. For the noncommutative analogue\, much less is known\,
with even the notion of "birational" not being very well understood. In pa
rticular\, although several constructions have been known (noncommutative
projective planes\, noncommutative ruled surfaces\, and noncommutative blo
wups)\, many basic isomorphisms have proved elusive (e.g.\, that blowups i
n distinct points commute). I'll discuss a new approach to the problem via
derived categories that not only makes it easy to construct the desired i
somorphisms but also to prove a number of other results\, in particular th
at anything birational to a ruled surface is either ruled or a projective
plane\, and the corresponding moduli spaces of simple sheaves are Poisson\
, with smooth symplectic leaves.\n
LOCATION:https://researchseminars.org/talk/Freemath/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takahiro Oba
DTSTART:20211102T100000Z
DTEND:20211102T110000Z
DTSTAMP:20260422T225755Z
UID:Freemath/60
DESCRIPTION:Title: A four-dimensional mapping class group relation\nby Takahiro Oba as
part of Free Mathematics Seminar\n\n\nAbstract\nRelations between Dehn twi
sts on mapping class groups of surfaces play an important role in the stud
y of symplectic manifolds via Lefschetz fibrations. In higher dimensions\,
as little is known about symplectic mapping class groups\, fibration-like
structures are not so powerful yet. In this talk\, I will give a relation
between 4-dimensional Dehn twists on a Weinstein domain. One of the key i
ngredients in the construction is a solution to the symplectic isotopy pro
blem for symplectic surfaces in a Del Pezzo surface.\n
LOCATION:https://researchseminars.org/talk/Freemath/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi Hong Chow
DTSTART:20211005T140000Z
DTEND:20211005T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/61
DESCRIPTION:Title: Homology of based loop groups and quantum cohomology of flag varieties\nby Chi Hong Chow as part of Free Mathematics Seminar\n\n\nAbstract\nK
be a compact Lie group and G its complexification. There are three ring ma
ps with the same source H_*(\\Omega K) and target QH(G/P) which arise from
the work of (1) Peterson/Lam-Shimozono\, (2) Seidel/Savelyev and (3) Ma'u
-Wehrheim-Woodward/Evans-Lekili respectively. In this talk\, I will discus
s how these maps are related and the applications.\n
LOCATION:https://researchseminars.org/talk/Freemath/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Engel
DTSTART:20211012T140000Z
DTEND:20211012T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/62
DESCRIPTION:Title: Compact K3 moduli\nby Philip Engel as part of Free Mathematics Semin
ar\n\n\nAbstract\nThe moduli space of polarized K3 surfaces is a non-compa
ct quotient of a symmetric space by an arithmetic group. In this capacity\
, it has an infinite class of combinatorially-defined "semitoroidal compac
tifications." I will discuss joint work with Valery Alexeev that sometimes
semitoroidal compactifications have geometric meaning: they parameterize
"stable K3 surfaces" in a way similar to how the Deligne-Mumford compactif
ication of curves parameterizes "stable curves." Inspired by ideas from mi
rror symmetry\, the semifan of such a compactification can sometimes be co
mputed\, using symplectic and integral-affine geometry.\n
LOCATION:https://researchseminars.org/talk/Freemath/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Min
DTSTART:20211026T140000Z
DTEND:20211026T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/63
DESCRIPTION:Title: Moduli space of symplectic log Calabi-Yau divisors and torus fibrations<
/a>\nby Jie Min as part of Free Mathematics Seminar\n\n\nAbstract\nSymplec
tic log Calabi-Yau divisors are the symplectic analogue of anti-canonical
divisors in algebraic geometry. We study the rigidity of such divisors. In
particular we prove a Torelli type theorem and form an equivalent moduli
space of homology configurations which is more suitable for counting. We a
lso discuss their relations to toric actions and almost toric fibrations\,
reprove a finiteness result and an upper bound for toric actions by Karsh
on-Kessler-Pinsonnault\, and prove a new stability result.\n
LOCATION:https://researchseminars.org/talk/Freemath/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angelica Simonetti
DTSTART:20211109T150000Z
DTEND:20211109T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/64
DESCRIPTION:by Angelica Simonetti as part of Free Mathematics Seminar\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/Freemath/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Pertusi
DTSTART:20211116T150000Z
DTEND:20211116T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/65
DESCRIPTION:Title: Serre-invariant stability conditions and cubic threefolds\nby Laura
Pertusi as part of Free Mathematics Seminar\n\n\nAbstract\nStability condi
tions on the Kuznetsov component of a Fano threefold of Picard rank 1\, in
dex 1 and 2 have been constructed by Bayer\, Lahoz\, Macrì and Stellari\,
making possible to study moduli spaces of stable objects and their geomet
ric properties. In this talk we investigate the action of the Serre functo
r on these stability conditions. In the index 2 case and in the case of GM
threefolds\, we show that they are Serre-invariant. Then we prove a gener
al criterion which ensures the existence of a unique Serre-invariant stabi
lity condition and applies to some of these Fano threefolds. Finally\, we
apply these results to the study of moduli spaces in the case of a cubic t
hreefold X. In particular\, we prove the smoothness of moduli spaces of st
able objects in the Kuznetsov component of X and the irreducibility of the
moduli space of stable Ulrich bundles on X. These results come from joint
works with Song Yang and with Soheyla Feyzbakhsh and in preparation with
Ethan Robinett.\n
LOCATION:https://researchseminars.org/talk/Freemath/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navid Nabijou
DTSTART:20211123T150000Z
DTEND:20211123T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/66
DESCRIPTION:Title: Enumerative invariants of 3-fold flops: hyperplane arrangements and wall
-crossing\nby Navid Nabijou as part of Free Mathematics Seminar\n\n\nA
bstract\n3-fold flopping contractions form a fundamental building block of
the higher-dimensional Minimal Model Program. They exhibit extremely rich
geometry\, which has been investigated by many people over the past half-
century. I will present an elegant and visually-pleasing relationship betw
een enumerative invariants of flopping contractions and certain hyperplane
arrangements constructed combinatorially from root system data. I will di
scuss both Gopakumar-Vafa (GV) and Gromov-Witten (GW) invariants\, explain
ing how these are related to one another and how they are encoded in finit
e and infinite arrangements\, respectively. Finally\, I will discuss wall-
crossing: our combinatorial approach allows us to explicitly construct flo
ps from root system data\, leading to a new “direct” proof of the Crep
ant Transformation Conjecture\, with a very explicit formulation. This is
joint work with Michael Wemyss.\n
LOCATION:https://researchseminars.org/talk/Freemath/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dogancan Karabas
DTSTART:20211130T150000Z
DTEND:20211130T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/67
DESCRIPTION:Title: Homotopy colimit formula for gluing wrapped Fukaya categories\, and lens
spaces\nby Dogancan Karabas as part of Free Mathematics Seminar\n\n\n
Abstract\nGanatra\, Pardon\, and Shende introduced a way to compute wrappe
d Fukaya categories of Weinstein domains by taking the homotopy colimit of
wrapped Fukaya categories of their sectorial coverings. However\, homotop
y colimits are hard to compute in general. In this talk\, I will describe
a practical formula for homotopy colimit when the categories are presented
as semifree dg categories. As an application\, I will show that the homot
opy type of lens spaces is detected by the wrapped Fukaya category of thei
r cotangent bundles. If time permits\, I will talk about other application
s of the formula\, such as the calculation of the wrapped Fukaya category
of plumbing spaces. This is joint work with Sangjin Lee.\n
LOCATION:https://researchseminars.org/talk/Freemath/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi
DTSTART:20211207T150000Z
DTEND:20211207T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/68
DESCRIPTION:Title: Entropy of autoequivalences and holomorphicity\nby Federico Barbacov
i as part of Free Mathematics Seminar\n\n\nAbstract\nThe notion of entropy
of an endofunctor categorifies the notion of topological entropy of a con
tinuous map. However\, while the latter is a number\, the former is a func
tion of a real variable. The value at zero of this function takes the name
of categorical entropy and makes the connection between the categorical a
nd the topological framework. In this talk I will report on joint work wit
h Jongmyeong Kim in which we give sufficient conditions for a conjecture i
n categorical dynamics (that mirrors a theorem of Gromov and Yomdin) to be
satisfied. Of particular interest is the fact that such conditions arise\
, through the philosophy of homological mirror symmetry\, as a categorific
ation of one of the properties of holomorphic functions.\n
LOCATION:https://researchseminars.org/talk/Freemath/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Seidel
DTSTART:20220125T150000Z
DTEND:20220125T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/69
DESCRIPTION:Title: Twisted open-closed string maps and applications\nby Paul Seidel as
part of Free Mathematics Seminar\n\n\nAbstract\n(This is joint work in pro
gress with Shaoyun Bai\, expanding on an idea of Sheel Ganatra). The nonde
generacy of the Shklyarov pairing gives an easy way to prove injectivity o
f the open-closed string map for Fukaya categories which are cohomological
ly smooth\, and that is also true in the case when it's twisted by a sympl
ectic automorphism. We will discuss some implications of this for Lefschet
z fibrations.\n
LOCATION:https://researchseminars.org/talk/Freemath/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Carocci
DTSTART:20220208T150000Z
DTEND:20220208T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/70
DESCRIPTION:Title: BPS invariant from non Archimedean integrals\nby Francesca Carocci a
s part of Free Mathematics Seminar\n\n\nAbstract\nWe consider moduli space
s M(ß\,χ) of one-dimensional semistable sheaves on del Pezzo and K3 sur
faces supported on ample curve classes. \nWorking over a non-archimedean l
ocal field F\, we define a natural measure on the F-points of such moduli
spaces. We prove that the integral of a certain naturally defined gerbe on
M(ß\,χ) with respect to this measure is independent of the Euler charac
teristic.\nAnalogous statements hold for (meromorphic or not) Higgs bundle
s.\nRecent results of Maulik-Shen and Kinjo-Coseki imply that these integr
als compute the BPS invariants for the del Pezzo case and for Higgs bundle
s.\nThis is a joint work with Giulio Orecchia and Dimitri Wyss.\n
LOCATION:https://researchseminars.org/talk/Freemath/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Woodward
DTSTART:20220301T150000Z
DTEND:20220301T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/71
DESCRIPTION:Title: Quantum stable manifolds for nearby Lagrangians\nby Chris Woodward a
s part of Free Mathematics Seminar\n\n\nAbstract\nAnalogs of Cohen-Jones-S
egal spaces for Lagrangian Floer cohomology of nearby Lagrangians naturall
y arise through a choice of quasi-isomorphisms\, and are cell complexes wi
th degree one evaluation maps to either Lagrangian. I will discuss some re
sults on the problem of desingularizing these classifying spaces.\n
LOCATION:https://researchseminars.org/talk/Freemath/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Petr
DTSTART:20220201T150000Z
DTEND:20220201T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/72
DESCRIPTION:Title: Invariant of the Legendrian lift of an exact Lagrangian submanifold in t
he circular contactization of a Liouville manifold\nby Adrian Petr as
part of Free Mathematics Seminar\n\n\nAbstract\nAny exact Lagrangian subma
nifold in a Liouville manifold lifts to a Legendrian submanifold in the ci
rcular contactization. For the standard contact form\, this Legendrian adm
its countably many Reeb chords (indexed by their winding number around the
fiber) above each point\, thus yielding a degenerate situation. In this t
alk\, we will slightly perturb the contact form and compute the Chekanov-E
liashberg DG-algebra of the Legendrian lift in term of the Floer A_{\\inft
y}-algebra of the Lagrangian. The main idea will be to view the Koszul dua
l of the DG-algebra as a particular homotopy colimit (as defined by Ganatr
a-Pardon-Shende) of A_{\\infty}-categories.\n
LOCATION:https://researchseminars.org/talk/Freemath/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel
DTSTART:20220215T150000Z
DTEND:20220215T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/73
DESCRIPTION:by Travis Mandel as part of Free Mathematics Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/Freemath/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin DeVleming
DTSTART:20220222T150000Z
DTEND:20220222T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/74
DESCRIPTION:Title: K-stability and birational geometry of moduli spaces of quartic K3 surfa
ces\nby Kristin DeVleming as part of Free Mathematics Seminar\n\n\nAbs
tract\nRecently it has been shown that K-stability provides well-behaved m
oduli spaces of Fano varieties and log Fano pairs\, and allows one to natu
rally interpolate between other geometric compactifications. I will discu
ss the picture for quartic K3 surfaces\, relating compactifications coming
from geometric invariant theory (GIT)\, Hodge theory\, and K-stability vi
a wall crossings in K-moduli. This is joint work with Kenneth Ascher and
Yuchen Liu.\n
LOCATION:https://researchseminars.org/talk/Freemath/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezra Getzler
DTSTART:20220308T150000Z
DTEND:20220308T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/75
DESCRIPTION:by Ezra Getzler as part of Free Mathematics Seminar\n\nAbstrac
t: TBA\n
LOCATION:https://researchseminars.org/talk/Freemath/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semon Rezchikov
DTSTART:20220315T150000Z
DTEND:20220315T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/76
DESCRIPTION:Title: Holomorphic Floer Theory and the Fueter Equation\nby Semon Rezchikov
as part of Free Mathematics Seminar\n\n\nAbstract\nThe Lagrangian Floer h
omology of a pair of holomorphic Lagrangian submanifolds of a hyperkahler
manifold is expected to simplify\, by work of Solomon-Verbitsky and others
. This occurs in part because\, in this setting\, the symplectic action fu
nctional\, the gradient flow of which computes Lagrangian Floer homology\,
is the real part of a holomorphic function. As noted by Haydys\, thinking
of this holomorphic function as a superpotential on an infinite-dimension
al symplectic manifold gives rise to a quaternionic analog of Floer's equa
tion for holomorphic strips: the Fueter equation. I will explain how this
line of thought gives rise to a `complexification' of Floer's theorem iden
tifying Fueter maps in cotangent bundles to Kahler manifolds with holomorp
hic planes in the base. This complexification has a conjectural categorica
l interpretation\, giving a model for Fukaya-Seidel categories of Lefshetz
fibrations\, which should have algebraic implications for the study of Fu
kaya categories. This is a report on upcoming joint work with Aleksander D
oan.\n
LOCATION:https://researchseminars.org/talk/Freemath/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Hilburn
DTSTART:20220322T150000Z
DTEND:20220322T160000Z
DTSTAMP:20260422T225755Z
UID:Freemath/77
DESCRIPTION:Title: Perverse Schobers and 2-Categorical 3d Mirror Symmetry\nby Justin Hi
lburn as part of Free Mathematics Seminar\n\n\nAbstract\n3d mirror symmetr
y predicts an equivalence between 2-categories associated to dual holomorp
hic symplectic stacks. The first 2-category is of an algebro-geometric fla
vor and has constructions due to Kapustin/Rozansky/Saulina and Arinkin. Th
e second category depends on symplectic topology and has a conjectural des
cription in terms of the 3d generalized Seiberg-Witten equations (also kno
wn as the gauged Fueter equations). \n\nIn this talk I will describe joint
work with Ben Gammage and Aaron Mazel-Gee proving a variant of 3d mirror
symmetry for Gale dual toric cotangent stacks. In particular\, we define a
combinatorial model for the symplectic 2-category using equivariant perve
rse schobers. If time permits I will explain work in progress extending ou
r equivalence from toric cotangent stacks to hypertoric varieties. This wi
ll provide a categorification of previous results on Koszul duality for hy
pertoric categories O.\n
LOCATION:https://researchseminars.org/talk/Freemath/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Fine
DTSTART:20220503T140000Z
DTEND:20220503T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/78
DESCRIPTION:Title: Knots\, minimal surfaces and J-holomorphic curves\nby Joel Fine as p
art of Free Mathematics Seminar\n\n\nAbstract\nLet K be a knot or link in
the 3-sphere\, thought of as the ideal boundary of hyperbolic 4-space\, H^
4. The main theme of my talk is that it should be possible to count minima
l surfaces in H^4 which fill K and obtain a link invariant. In other words
\, the count doesn’t change under isotopies of K. When one counts minima
l disks\, this is a theorem. Unfortunately there is currently a gap in the
proof for more complicated surfaces. I will explain “morally” why the
result should be true and how I intend to fill the gap. In fact\, this (c
urrently conjectural) invariant is a kind of Gromov—Witten invariant\, c
ounting J-holomorphic curves in a certain symplectic 6-manifold diffeomorp
hic to S^2xH^4. The symplectic structure becomes singular at infinity\, in
directions transverse to the S^2 fibres. These singularities mean that bo
th the Fredholm and compactness theories have fundamentally new features\,
which I will describe. Finally\, there is a whole class of infinite-volum
e symplectic 6-manifolds which have singularities modelled on the above si
tuation. I will explain how it should be possible to count J-holomorphic c
urves in these manifolds too\, and obtain invariants for links in other 3-
manifolds.\n
LOCATION:https://researchseminars.org/talk/Freemath/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria di Dedda
DTSTART:20220510T140000Z
DTEND:20220510T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/79
DESCRIPTION:Title: Realising perfect derived categories of Auslander algebras of type A as
Fukaya-Seidel categories\nby Ilaria di Dedda as part of Free Mathemati
cs Seminar\n\n\nAbstract\nThe theme of this talk will be to build a bridge
between two areas of mathematics: representation theory and symplectic ge
ometry. Our objects of interest on the representation theoretical side are
Auslander algebras of type A. This family of non-commutative algebras ari
ses very naturally as endomorphism algebras of indecomposable modules of q
uivers of finite type. They were given a symplectic interpretation by Dyck
erhoff-Jasso-Lekili\, who proved the equivalence (as $A_{\\infty}$-categor
ies) between perfect derived categories of Auslander algebras of type A an
d certain partially wrapped Fukaya categories. We use their result to prov
e an equivalence between the categories in question and the Fukaya-Seidel
categories of a certain family of Lefschetz fibrations. In this talk\, we
will observe this result in some key examples.\n
LOCATION:https://researchseminars.org/talk/Freemath/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riccardo Pedrotti
DTSTART:20220517T140000Z
DTEND:20220517T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/80
DESCRIPTION:Title: Fixed point Floer cohomology of a Dehn twist in a monotone setting and i
n more general contexts\nby Riccardo Pedrotti as part of Free Mathemat
ics Seminar\n\n\nAbstract\nIn this talk we will talk about the fixed point
Floer cohomology of a Dehn twist. Nowadays there are several methods to c
ompute it\, for example by using the Seidel exact triangle. Inspired by an
early result of P. Seidel (1996) for twists on surfaces\, we gave an expl
icit description of the Floer cohomology of a Dehn twist in terms of Morse
cohomology of some “sub-quotients” of M. The main step will be to use
a neck-stretching argument to establish some energy lower bounds on certa
in trajectories realising differentials. We will start by studying the rat
her restricting yet convenient “strongly - monotone” case and then sho
w how to generalise it to more general settings using an energy filtration
argument due to K. Ono. Time permitting\, we will sketch an application o
f our techniques in the context of ongoing joint work with T. Perutz\n
LOCATION:https://researchseminars.org/talk/Freemath/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Kegel
DTSTART:20220524T140000Z
DTEND:20220524T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/81
DESCRIPTION:Title: Stein traces\nby Marc Kegel as part of Free Mathematics Seminar\n\n\
nAbstract\nEvery Legendrian knot leaves a traces in the 4-dimensional symp
lectic world. In this talk we will investigate whether a 4-dimensional tra
cker (with the necessary mathematical education) can determine the 3-dimen
sional creature that left the trace. This is based on joint work with Roge
r Casals and John Etnyre.\n
LOCATION:https://researchseminars.org/talk/Freemath/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Li
DTSTART:20220614T140000Z
DTEND:20220614T150000Z
DTSTAMP:20260422T225755Z
UID:Freemath/82
DESCRIPTION:Title: The Thomas-Yau conjecture\nby Yang Li as part of Free Mathematics Se
minar\n\n\nAbstract\nThe Thomas-Yau conjecture is an open-ended program to
relate special Lagrangians to stability conditions in Floer theory\, but
the precise notion of stability is subject to many interpretations. I will
focus on the exact case (Stein Calabi-Yau manifolds)\, and deal only with
almost calibrated Lagrangians. We will discuss how the existence of desta
bilising exact triangles obstructs special Lagrangians\, under some additi
onal assumptions\, using the technique of integration over moduli spaces.\
n
LOCATION:https://researchseminars.org/talk/Freemath/82/
END:VEVENT
END:VCALENDAR