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BEGIN:VEVENT
SUMMARY:Gao Chen (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20200909T200000Z
DTEND;VALUE=DATE-TIME:20200909T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/1
DESCRIPTION:Title: T
he J-equation\, dHYM equation\, and cscK metrics\nby Gao Chen (Univers
ity of Wisconsin-Madison) as part of Boston University Geometry/Physics Se
minar\n\n\nAbstract\nThe deformed Hermitian-Yang-Mills (dHYM) equation is
the mirror equation for the special Lagrangian equation. The "small radius
limit" of the dHYM equation is the J-equation\, which is closely related
to the constant scalar curvature K\\"ahler (cscK) metrics. In this talk\,
I will explain my recent result that the solvability of the J-equation is
equivalent to a notion of stability. I will also explain my similar resul
t on the supercritical dHYM equation as well as the application of my resu
lts to the cscK problem.\n
LOCATION:https://researchseminars.org/talk/BUGeom/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Engel (University of Georgia)
DTSTART;VALUE=DATE-TIME:20200916T200000Z
DTEND;VALUE=DATE-TIME:20200916T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/2
DESCRIPTION:Title: C
ompactification of K3 moduli\nby Philip Engel (University of Georgia)
as part of Boston University Geometry/Physics Seminar\n\n\nAbstract\nBy th
e Torelli theorem\, the moduli space of lattice polarized K3 surfaces is\n
the quotient of a Hermitian symmetric domain by an arithmetic group. In th
is capacity\,\nit has compactifications such as the Baily-Borel and toroid
al compactifications\nwhich depend on some choice of fan. On the other han
d\, choosing canonically an ample\ndivisor on every such K3\, one can buil
d a compactification via so-called (KSBA) stable pairs.\nI will discuss jo
int work with V. Alexeev on how one proves that the normalization of\na st
able pair compactification of K3 moduli is the toroidal compactification \
nfor an appropriate choice of fan. We will focus on the example of ellipti
c K3s\, polarized\nby the section plus the sum of the singular fibers.\n
LOCATION:https://researchseminars.org/talk/BUGeom/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Woodward (Rutgers University)
DTSTART;VALUE=DATE-TIME:20200923T200000Z
DTEND;VALUE=DATE-TIME:20200923T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/3
DESCRIPTION:Title: F
ukaya Categories of Blow-ups\nby Chris Woodward (Rutgers University) a
s part of Boston University Geometry/Physics Seminar\n\n\nAbstract\nThis i
s joint work with Venugopalan and Xu. \nIn good cases\, we construct split
-generators for the Fukaya category of sufficiently small symplectic blow-
ups. For example\, for iterated blow-ups of projective spaces this implie
s an affirmative answer to Kontsevich's question on the relation \nbetween
quantum cohomology and Hochschild cohomology of the Fukaya category.\n
LOCATION:https://researchseminars.org/talk/BUGeom/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hang Yuan (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20200930T200000Z
DTEND;VALUE=DATE-TIME:20200930T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/4
DESCRIPTION:Title: F
amily Floer theory for toric manifolds\nby Hang Yuan (Stony Brook Univ
ersity) as part of Boston University Geometry/Physics Seminar\n\n\nAbstrac
t\nGiven a Lagrangian fibration\, my recent work gives a natural construct
ion of a rigid analytic space and a global Landau-Ginzburg potential\, bas
ed on Fukaya’s family Floer theory and non-archimedean geometry.\n In th
is talk\, I will discuss my work in progress\, which explains how to apply
this construction to the toric manifolds. Specifically\, I will discuss t
he moment map fibration on a toric manifold and the Gross’s fibration on
a toric Calabi-Yau manifold. I will explain how the outcomes are related
to the previous works of Cho-Oh\, Fukaya-Oh-Ohta-Ono\, Chan-Lau-Leung\, an
d Abouzaid-Auroux-Katzarkov.\n
LOCATION:https://researchseminars.org/talk/BUGeom/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guangbo Xu (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20201007T200000Z
DTEND;VALUE=DATE-TIME:20201007T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/5
DESCRIPTION:Title: C
ompactness of instantons and the Atiyah-Floer conjecture\nby Guangbo X
u (Texas A&M University) as part of Boston University Geometry/Physics Sem
inar\n\n\nAbstract\nThe Atiyah-Floer conjecture says that the instanton Fl
oer homology of a three-manifold (constructed via gauge theory) agrees wit
h a Lagrangian Floer homology (constructed via symplectic geometry) associ
ated to a splitting of the manifold. Atiyah's heuristic argument of this c
onjecture relies on a compactness result for instantons in a certain adiab
atic limit. I will present a proof of such a compact theorem for the case
when the gauge group is SO(3)\, as well as another compactness theorem rel
ated to bounding chains on the symplectic side.\n
LOCATION:https://researchseminars.org/talk/BUGeom/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jordan (University of Edingburgh)
DTSTART;VALUE=DATE-TIME:20201014T200000Z
DTEND;VALUE=DATE-TIME:20201014T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/6
DESCRIPTION:Title: C
luster quantization of character stacks as a singular topological field th
eory\nby David Jordan (University of Edingburgh) as part of Boston Uni
versity Geometry/Physics Seminar\n\n\nAbstract\nCharacter stacks are certa
in moduli spaces of G-local systems on a manifold\, which arise naturally
in both 4d N=4 Kapustin-Witten and 3d N=4 Sicilian gauge theories. Their
quantizations relate to deforming the coupling parameter\, and introducing
omega-deformation\, respectively. Fock and Goncharov have introduced a m
odification of character varieties\, in which the G-local systems are deco
rated with parabolic reductions along fixed regions of the surface\, and o
n these decorated character varieties they have exhibited cluster structur
es. This means\, there is a family of open subsets\, indexed combinatoria
lly\, on which the stack is actually an algebraic torus. The transitions
between charts are given by certain explicit birational transformations ca
lled mutations. Finally\, they have defined a quantization of this structu
re\, which has a number of remarkable properties.\n\nIn this talk I will e
xplain how to upgrade their construction to a fully extended topological f
ield theory using the framework of stratified factorization homology devel
oped by Ayala-Francis-Tanaka.\n
LOCATION:https://researchseminars.org/talk/BUGeom/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of California\, Davis/ University of Edi
ngurgh)
DTSTART;VALUE=DATE-TIME:20201021T200000Z
DTEND;VALUE=DATE-TIME:20201021T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/7
DESCRIPTION:Title: 3
d A & B models\, mirror symmetry\, and HOMFLY homology\nby Tudor Dimof
te (University of California\, Davis/ University of Edingurgh) as part of
Boston University Geometry/Physics Seminar\n\n\nAbstract\nI will review so
me what's known about topological A and B twists of 3d N=4 supersymmetric
gauge theories\, in particular the algebraic/categorical structures that t
hey contain. The physical duality known as 3d mirror symmetry exchanges 3d
A and B twists\, and should manifest mathematically as a higher analogue
of homological mirror symmetry. I will then explain how these ideas may be
concretely applied to reproduce and connect several different constructio
ns of HOMFLY-PT homology (soon to appear in work with Garner\, Hilburn\, O
blomkov\, and Rozansky).\n
LOCATION:https://researchseminars.org/talk/BUGeom/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Pomerleano (University of Massachusetts\, Boston)
DTSTART;VALUE=DATE-TIME:20201028T200000Z
DTEND;VALUE=DATE-TIME:20201028T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/8
DESCRIPTION:Title: I
ntrinsic Mirror Symmetry and Categorical Crepant Resolutions\nby Danie
l Pomerleano (University of Massachusetts\, Boston) as part of Boston Univ
ersity Geometry/Physics Seminar\n\n\nAbstract\nA general expectation in mi
rror symmetry is that the mirror partner to an affine log Calabi-Yau varie
ty is "algebraically convex" (meaning it is proper over its affinization).
We will describe work in progress which shows how this algebraic convexit
y of the mirror manifests itself directly as certain finiteness properties
of Floer theoretic invariants of X (the symplectic cohomology and wrapped
Fukaya category). As an application of these finiteness results\, we will
show that for maximally degenerate log Calabi-Yau varieties equipped with
a ``homological section\," the wrapped Fukaya of X gives an (intrinsic) c
ategorical crepant resolution of the affine variety Spec($SH^0(X)$).\n
LOCATION:https://researchseminars.org/talk/BUGeom/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Fredrickson (University of Oregon)
DTSTART;VALUE=DATE-TIME:20201105T210000Z
DTEND;VALUE=DATE-TIME:20201105T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/9
DESCRIPTION:Title: T
he Asymptotic geometry of the Hitchin moduli space\nby Laura Fredricks
on (University of Oregon) as part of Boston University Geometry/Physics Se
minar\n\n\nAbstract\nHitchin's equations are a system of gauge theoretic e
quations on a Riemann surface that are of interest in many areas including
representation theory\, Teichm\\"uller theory\, and the geometric Langlan
ds correspondence. The Hitchin moduli space carries a natural hyperk\\"ahl
er metric. An intricate conjectural description of its asymptotic structu
re appears in the work of physicists Gaiotto-Moore-Neitzke and there has b
een a lot of progress on this recently. I will discuss some recent result
s using tools coming out of geometric analysis which are well-suited for v
erifying these extremely delicate conjectures. This strategy often stretch
es the limits of what can currently be done via\ngeometric analysis\, and
simultaneously leads to new insights into these conjectures.\n
LOCATION:https://researchseminars.org/talk/BUGeom/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Gibney (Rutgers University)
DTSTART;VALUE=DATE-TIME:20201111T210000Z
DTEND;VALUE=DATE-TIME:20201111T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/10
DESCRIPTION:Title:
Vertex algebras of CohFT-type\nby Angela Gibney (Rutgers University) a
s part of Boston University Geometry/Physics Seminar\n\n\nAbstract\nRepres
entations of vertex algebras of CohFT-type can be used to construct vector
bundles of coinvariants and conformal blocks on moduli spaces of stable p
ointed curves. The name comes from the fact they define semisimple cohomol
ogical field theories. I’ll say something about why one may be intereste
d in these bundles and their classes\, and give some examples. This is abo
ut work with Chiara Damiolini and Nicola Tarasca.\n
LOCATION:https://researchseminars.org/talk/BUGeom/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hicks (Cambridge University)
DTSTART;VALUE=DATE-TIME:20201118T210000Z
DTEND;VALUE=DATE-TIME:20201118T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/11
DESCRIPTION:Title:
Lagrangian submanifolds in almost toric fibrations\nby Jeff Hicks (Cam
bridge University) as part of Boston University Geometry/Physics Seminar\n
\n\nAbstract\nMirror symmetry predicts that Lagrangian submanifolds of a s
ymplectic space X are mirror to coherent sheaves on a ``mirror space'' Y.
A proposed mechanism for mirror symmetry comes from almost Lagrangian toru
s fibrations. In this framework\, X and Y are dual Lagrangian torus fibrat
ions over a common affine base Q. Mirror symmetry arises by degenerating t
he symplectic geometry of X and complex geometry of Y to tropical geometry
on the base Q. We will look at the setting where X is the complement of t
he elliptic curve in the projective plane\, and discuss how to construct L
agrangian submanifolds of X from the data of tropical curves in the base o
f the fibration.\n
LOCATION:https://researchseminars.org/talk/BUGeom/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bouseau (CNRS\, Universite Paris Saclay)
DTSTART;VALUE=DATE-TIME:20201202T210000Z
DTEND;VALUE=DATE-TIME:20201202T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/12
DESCRIPTION:Title:
Positivity for the skein algebra of the 4-puncture sphere\nby Pierrick
Bouseau (CNRS\, Universite Paris Saclay) as part of Boston University Geo
metry/Physics Seminar\n\n\nAbstract\nThe skein algebra of a topological su
rface is constructed from knots and links in the 3-manifold obtained by ta
king the product of the surface with an interval. A conjecture of Dylan Th
urston predicts the positivity of the structure constants of a certain lin
ear basis of the skein algebra. I will explain a recent proof of this conj
ecture for the skein algebra of the 4-punctured sphere. In a slightly surp
rising way\, this proof of a topological result relies on complex algebrai
c geometry\, and in particular the study of algebraic curves in complex cu
bic surfaces.\n
LOCATION:https://researchseminars.org/talk/BUGeom/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hulya Arguz (University of Versailles - Paris Saclay)
DTSTART;VALUE=DATE-TIME:20201209T210000Z
DTEND;VALUE=DATE-TIME:20201209T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/13
DESCRIPTION:Title:
Computing punctured log Gromov--Witten invariants via wall-crossing\nb
y Hulya Arguz (University of Versailles - Paris Saclay) as part of Boston
University Geometry/Physics Seminar\n\nAbstract: TBA\n\nComputing puncture
d log Gromov--Witten invariants via wall-crossing \nAbstract: Punctured lo
g Gromov—Witten invariants of Abramovich—Chen--Gross—Siebert are obt
ained by counting stable maps with prescribed tangency conditions (which a
re allowed to be negative) relative to a not necessarily smooth divisor. W
e provide a technique based on tropical geometry and wall-crossing algorit
hms to compute punctured log Gromov-Witten invariants of log Calabi-Yau va
rieties which are obtained by blowing-up of toric varieties along hypersur
faces on the toric boundary. This is joint work with Mark Gross (arxiv:200
7.08347).\n
LOCATION:https://researchseminars.org/talk/BUGeom/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentino Tosatti (McGill University)
DTSTART;VALUE=DATE-TIME:20210127T210000Z
DTEND;VALUE=DATE-TIME:20210127T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/14
DESCRIPTION:Title:
Smooth asymptotics for collapsing Ricci-flat metrics\nby Valentino Tos
atti (McGill University) as part of Boston University Geometry/Physics Sem
inar\n\nLecture held in Zoom meeting ID: 974 5641 9902.\n\nAbstract\nI wil
l discuss the problem of understanding the collapsing behavior of Ricci-fl
at Kahler metrics on a Calabi-Yau manifold that admits a holomorphic fibra
tion structure\, when the Kahler class degenerates to the pullback of a Ka
hler class from the base. I will present new work with Hans-Joachim Hein w
here we obtain a priori estimates of all orders for the Ricci-flat metrics
away from the singular fibers\, as a corollary of a complete asymptotic e
xpansion.\n
LOCATION:https://researchseminars.org/talk/BUGeom/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Payne (University of Texas\, Austin)
DTSTART;VALUE=DATE-TIME:20210210T210000Z
DTEND;VALUE=DATE-TIME:20210210T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/15
DESCRIPTION:Title:
Top weight cohomology of M_g\nby Sam Payne (University of Texas\, Aust
in) as part of Boston University Geometry/Physics Seminar\n\nLecture held
in Zoom meeting ID: 974 5641 9902.\n\nAbstract\nI will discuss an approach
to studying the top-graded piece of the weight filtration on open moduli
spaces with suitable toroidal compactifications\, inspired by tropical and
non-archimedean analytic geometry. One application of this approach is t
he recent proof\, joint with Chan and Galatius\, that the dimension of H^{
4g-6}(M_g\, Q) grows exponentially with g. This growth was unexpected and
disproves conjectures of Church-Farb-Putman and Kontsevich.\n
LOCATION:https://researchseminars.org/talk/BUGeom/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Yue Yu (Université Paris-Sud\, Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20210217T190000Z
DTEND;VALUE=DATE-TIME:20210217T200000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/16
DESCRIPTION:Title:
Frobenius structure conjecture and application to cluster algebras\nby
Tony Yue Yu (Université Paris-Sud\, Paris-Saclay) as part of Boston Univ
ersity Geometry/Physics Seminar\n\nLecture held in Zoom meeting ID: 974 56
41 9902.\n\nAbstract\nI will explain the Frobenius structure conjecture of
Gross-Hacking-Keel in mirror symmetry\, and an application towards cluste
r algebras. Let U be an affine log Calabi-Yau variety containing an open a
lgebraic torus. We show that the naive counts of rational curves in U uniq
uely determine a commutative associative algebra equipped with a compatibl
e multilinear form. Although the statement of the theorem involves only el
ementary algebraic geometry\, the proof employs Berkovich non-archimedean
analytic methods. We construct the structure constants of the algebra via
counting non-archimedean analytic disks in the analytification of U. I wil
l explain various properties of the counting\, notably deformation invaria
nce\, symmetry\, gluing formula and convexity. In the special case when U
is a Fock-Goncharov skew-symmetric X-cluster variety\, our algebra general
izes\, and gives a direct geometric construction of\, the mirror algebra o
f Gross-Hacking-Keel-Kontsevich. The comparison is proved via a canonical
scattering diagram defined by counting infinitesimal non-archimedean analy
tic cylinders\, without using the Kontsevich-Soibelman algorithm. Several
combinatorial conjectures of GHKK\, as well as the positivity in the Laure
nt phenomenon\, follow readily from the geometric description. This is joi
nt work with S. Keel\, arXiv:1908.09861. If time permits\, I will mention
another application towards the moduli space of KSBA (Kollár-Shepherd-Bar
ron-Alexeev) stable pairs\, joint with P. Hacking and S. Keel\, arXiv: 200
8.02299.\n
LOCATION:https://researchseminars.org/talk/BUGeom/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hariharan Narayanan (Tata Institute for Fundamental Research)
DTSTART;VALUE=DATE-TIME:20210224T160000Z
DTEND;VALUE=DATE-TIME:20210224T170000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/17
DESCRIPTION:Title:
Testing the manifold hypothesis and fitting a manifold of large reach to n
oisy data\nby Hariharan Narayanan (Tata Institute for Fundamental Rese
arch) as part of Boston University Geometry/Physics Seminar\n\nLecture hel
d in Zoom meeting ID: 974 5641 9902.\n\nAbstract\nThe hypothesis that high
dimensional data tend to lie in the vicinity of a low dimensional manifol
d is the basis of manifold learning. \nWe will discuss a joint work with C
harles Fefferman and Sanjoy Mitter on testing the manifold hypothesis. We
will outline an algorithm (with accompanying complexity guarantees) for fi
tting a manifold to an unknown probability distribution supported in a sep
arable Hilbert space\, only using i.i.d samples from that distribution.\nW
e also give a solution based on joint work with Charles Fefferman\, Sergei
Ivanov and Matti Lassas to the following question from manifold learning.
\nSuppose data belonging to a high dimensional Euclidean space is sampled
independently\, identically at random\, from a measure supported on a d di
mensional twice differentiable embedded manifold M\, and corrupted by Gaus
sian noise with small standard deviation sigma. How can we produce a manif
old M_o whose Hausdorff distance to M is small and whose reach (normal inj
ectivity radius) is not much smaller than the reach of M? We show how to p
roduce a manifold within O(sigma^2) of M in Hausdorf distance\, whose reac
h is smaller than that of M by a factor of no more than O(d^6).\n
LOCATION:https://researchseminars.org/talk/BUGeom/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suvrit Sra (MIT)
DTSTART;VALUE=DATE-TIME:20210303T204500Z
DTEND;VALUE=DATE-TIME:20210303T214500Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/18
DESCRIPTION:Title:
Accelerated gradient methods on Riemannian manifolds\nby Suvrit Sra (M
IT) as part of Boston University Geometry/Physics Seminar\n\nLecture held
in Zoom meeting ID: 974 5641 9902.\n\nAbstract\nThis talk lies at the inte
rface of geometry and optimization. I'll talk about geodesically convex op
timization problems\, a rich class of non-convex optimization problems tha
t admit tractable global optimization. I'll provide some background on thi
s class and some motivating examples. Beyond a general introduction to the
topic area\, I will dive deeper into a recent discovery of a long-sought
result: an accelerated gradient method for Riemannian manifolds. Towards d
eveloping this method\, we will revisit Nesterov's (Euclidean) estimate se
quence technique and present a conceptually simple alternative. We will th
en generalize this simpler alternative to the Riemannian setting. Combined
with a new geometric inequality\, we will then obtain the first (global)
accelerated Riemannian-gradient method. I'll also comment on some very rec
ent updates on this topic.\n
LOCATION:https://researchseminars.org/talk/BUGeom/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Schiffmann (Université de Paris-Sud ORSAY)
DTSTART;VALUE=DATE-TIME:20210317T200000Z
DTEND;VALUE=DATE-TIME:20210317T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/19
DESCRIPTION:Title:
Cohomological Hall algebras\, Yangians and Kleinian surface singularities<
/a>\nby Olivier Schiffmann (Université de Paris-Sud ORSAY) as part of Bos
ton University Geometry/Physics Seminar\n\nLecture held in Zoom meeting ID
: 974 5641 9902.\n\nAbstract\nModuli spaces of sheaves on complex surfaces
play an important role in algebraic geometry\, with motivation coming fro
m (among others) string theory and gauge theory.\n\nOne way to understand
the structure of the cohomology of such moduli spaces is to construct an a
ction of a suitable algebra\, through some 'Hecke type' correspondences. T
raditionally\, one considers Hecke correspondences modifying a sheaf at a
single point (varying along a fixed cycle on the surface). In an ongoing j
oint work with Diaconescu\, Sala and Vasserot\, we consider the case of re
solutions of Kleinian singularities\, and modifications along the (1-dimen
sional) components of the exceptional locus. This yields actions of some Y
angian type algebras (more precisely\, affine Yangians). The main tool is
the notion of cohomological Hall algebra\, and the main technical result d
escribes the behavior of such algebras upon derived equivalences coming fr
om reflection functors.\n
LOCATION:https://researchseminars.org/talk/BUGeom/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Neitzke (Yale University)
DTSTART;VALUE=DATE-TIME:20210331T200000Z
DTEND;VALUE=DATE-TIME:20210331T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/20
DESCRIPTION:Title:
An update on hyperkahler metrics on moduli of Higgs bundles\nby Andy N
eitzke (Yale University) as part of Boston University Geometry/Physics Sem
inar\n\nLecture held in Zoom meeting ID: 974 5641 9902.\n\nAbstract\nIn jo
int work with Davide Gaiotto and Greg Moore\, we gave a\nconjectural const
ruction of the hyperkahler metric on moduli spaces of Higgs\nbundles. The
key new ingredients in this construction are counts of BPS states\n(Donald
son-Thomas-type invariants).\n\nThrough the work of various authors\, incl
uding me\, Dumas\, Fredrickson\,\nMazzeo\, Swoboda\, Weiss\, Witt\, there
is now some evidence that this\nconjectural picture is correct. On the one
hand\, some of the asymptotic\npredictions which follow from the conjectu
re have been proven\; on the other\nhand\, there is numerical evidence tha
t the conjecture is correct even far\naway from the asymptotic limit. I wi
ll review these developments.\n
LOCATION:https://researchseminars.org/talk/BUGeom/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel (University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20210310T210000Z
DTEND;VALUE=DATE-TIME:20210310T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/21
DESCRIPTION:Title:
Tropical multiplicities from polyvector fields and QFT\nby Travis Mand
el (University of Oklahoma) as part of Boston University Geometry/Physics
Seminar\n\nLecture held in Zoom meeting ID: 974 5641 9902.\n\nAbstract\nWh
en considering planar tropical curves satisfying point conditions\, Mikhal
kin expressed the tropical curves' multiplicities as the product of the mu
ltiplicities of their vertices. Such a decomposition of the multiplicity
into local computations is very useful in practice\, e.g.\, in the Gross-S
iebert program. I will describe joint work with H. Ruddat in which we giv
e such localized tropical multiplicity formulas very generally (in genus 0
) using mirror polyvector fields. Our approach involves developing a noti
on of tropical quantum field theory which works for all genera.\n
LOCATION:https://researchseminars.org/talk/BUGeom/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheuk Yu Mak (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20210203T210000Z
DTEND;VALUE=DATE-TIME:20210203T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/22
DESCRIPTION:Title:
Non-displaceable Lagrangian links in four-manifolds\nby Cheuk Yu Mak (
University of Edinburgh) as part of Boston University Geometry/Physics Sem
inar\n\nLecture held in Zoom meeting ID: 974 5641 9902.\n\nAbstract\nOne o
f the earliest fundamental applications of Lagrangian Floer theory is dete
cting the non-displaceablity of a Lagrangian submanifold. Many progress a
nd generalisations have been made since then but little is known when the
Lagrangian submanifold is disconnected. In this talk\, we describe a new
idea to address this problem. Subsequently\, we explain how to use Fukaya
-Oh-Ohta-Ono and Cho-Poddar theory to show that for every S^2 \\times S^2
with a non-monotone product symplectic form\, there is a continuum of disc
onnected\, non-displaceable Lagrangian submanifolds such that each connect
ed component is displaceable. This is a joint work with Ivan Smith.\n
LOCATION:https://researchseminars.org/talk/BUGeom/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (Stanford University)
DTSTART;VALUE=DATE-TIME:20210324T200000Z
DTEND;VALUE=DATE-TIME:20210324T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/23
DESCRIPTION:Title:
Computations in relative symplectic cohomology\nby Umut Varolgunes (St
anford University) as part of Boston University Geometry/Physics Seminar\n
\nLecture held in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nThis is joi
nt work with Yoel Groman. I will present some computations of relative sym
plectic cohomology for pre-images of compact subsets in bases of certain L
agrangian torus fibrations. I will then explain how these computations lea
d to constructions of non-archimedean mirrors with expected properties. In
particular\, I will explain the relevance of the locality theorem that we
are currently finishing writing up and the Mayer-Vietoris property that I
had proven in my thesis.\n
LOCATION:https://researchseminars.org/talk/BUGeom/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Gualtieri (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210505T200000Z
DTEND;VALUE=DATE-TIME:20210505T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/24
DESCRIPTION:by Marco Gualtieri (University of Toronto) as part of Boston U
niversity Geometry/Physics Seminar\n\nLecture held in Zoom meeting ID: 953
4652 9200.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BUGeom/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20210407T200000Z
DTEND;VALUE=DATE-TIME:20210407T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/25
DESCRIPTION:Title:
Kapustin—Witten TQFT on 3-manifolds and derived skein modules\nby Pa
vel Safronov (University of Edinburgh) as part of Boston University Geomet
ry/Physics Seminar\n\nLecture held in Zoom meeting ID: 953 4652 9200.\n\nA
bstract\nKapustin and Witten have proposed that there is a 4-dimensional T
QFT underlying the geometric Langlands program and have described it as a
topological twist of the 4-dimensional maximally supersymmetric Yang—Mil
ls theory. In this talk I will discuss some mathematically-rigorous ways t
o define the space of states for 3-manifolds\, relating it to skein module
s and complexified instanton Floer homology of Abouzaid—Manolescu. I wil
l also comment on the possible extension of the geometric Langlands dualit
y to 3-manifolds. This is based on work in progress with D. Jordan and S.
Gunningham.\n
LOCATION:https://researchseminars.org/talk/BUGeom/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Lazarev (Columbia University)
DTSTART;VALUE=DATE-TIME:20210414T200000Z
DTEND;VALUE=DATE-TIME:20210414T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/26
DESCRIPTION:Title:
Inverting primes in symplectic geometry\nby Oleg Lazarev (Columbia Uni
versity) as part of Boston University Geometry/Physics Seminar\n\nLecture
held in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nA classical construct
ion in topology associates to a space X and prime p\, a new "localized" sp
ace X_p whose homotopy and homology groups are obtained from those of X by
inverting p. In this talk\, I will discuss a symplectic analog of this co
nstruction and explain how it interpolates between "flexible" and "rigid"
symplectic manifolds. \n\nConcretely\, I will produce prime-localized Wein
stein subdomains of high-dimensional Weinstein domains (which can be thou
ght of as singular Lagrangians) and show that any Weinstein subdomain of a
cotangent bundle agrees Fukaya-categorically with one of these special su
bdomains. The key will be to classify which objects of the Fukaya category
of T*M - twisted complexes of Lagrangians - are quasi-isomorphic to actua
l Lagrangians. This talk is based on joint work with Zach Sylvan and Hiro
Lee Tanaka.\n
LOCATION:https://researchseminars.org/talk/BUGeom/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Armenta (Université de Sherbrooke\, Sherbrooke)
DTSTART;VALUE=DATE-TIME:20210421T200000Z
DTEND;VALUE=DATE-TIME:20210421T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/27
DESCRIPTION:Title:
Derived invariance of operations in Hochschild theory\nby Marco Arment
a (Université de Sherbrooke\, Sherbrooke) as part of Boston University Ge
ometry/Physics Seminar\n\nLecture held in Zoom meeting ID: 953 4652 9200.\
n\nAbstract\nIn this talk\, I will introduce Hochschild homology and cohom
ology\, together with the well-known operations cup product and Gerstenhab
er bracket\, and the not-so-known cap product and Connes differential. I w
ill explain how all these operations can be interpreted inside the derived
category of the algebra which allows proving derived invariance of the wh
ole structure\, known as a Tamarkin-Tsygan calculus or a differential calc
ulus. Finally\, I will show how this construction is functorial in the alg
ebra using cyclic homology\, and give an example showing that the Tamarkin
-Tsygan calculus is not a complete derived invariant\, by means of quivers
and the Coxeter polynomial. This is joint work with Bernhard Keller.\n
LOCATION:https://researchseminars.org/talk/BUGeom/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Gualtieri (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210428T200000Z
DTEND;VALUE=DATE-TIME:20210428T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/28
DESCRIPTION:Title:
Branes\, Groupoids\, and Quantization\nby Marco Gualtieri (University
of Toronto) as part of Boston University Geometry/Physics Seminar\n\nLectu
re held in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nIn the past few ye
ars\, new light has been shed on the notion of\ngeneralized Kahler geometr
y\, by using ideas from the Weinstein school\nof Poisson geometry. We now
understand that the generalized Kahler\nmetric may be viewed as an imagina
ry Lagrangian submanifold in a\nholomorphic symplectic groupoid which enco
des the pair of holomorphic\nPoisson structures underlying the generalized
Kahler structure.\nAfter explaining how this mechanism works\, I will sho
w how it leads to\na method for quantizing certain holomorphic Poisson str
uctures in a\nfashion similar to that used in the work of Gukov and Witten
on\ngeometric quantization. This is an ongoing joint work with Francis\n
Bischoff.\n
LOCATION:https://researchseminars.org/talk/BUGeom/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miranda Cheng (Academia Sinica/University of Amsterdam)
DTSTART;VALUE=DATE-TIME:20210915T150000Z
DTEND;VALUE=DATE-TIME:20210915T160000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/29
DESCRIPTION:Title:
Three-Manifolds\, Quantum Modular Forms and log VOAs\nby Miranda Cheng
(Academia Sinica/University of Amsterdam) as part of Boston University Ge
ometry/Physics Seminar\n\nLecture held in Zoom meeting ID: 937 3195 9866.\
n\nAbstract\nQuantum modular forms are\, roughly speaking\, functions that
have certain weak modular properties. Mock modular forms and false theta
functions are examples of holomorphic functions on the upper-half plane wh
ich lead to quantum modular forms. Generalising the Witten-Reshetikhin-Tur
aev invariants for three-manifolds which arise from Chern-Simons theory\,
a new topological invariant named homological blocks which arise from 6d S
CFT have been proposed a few years ago. My talk aims to explain the recent
observations on the quantum modular properties of the homological blocks\
, as well as the relation to logarithmic vertex algebras. The talk will be
based on a series of work in collaboration with Sungbong Chun\, Ioana Com
an Lohi\, Boris Feigin\, Francesca Ferrari\, Sergei Gukov\, Sarah Harrison
\, Davide Passaro\, and Gabriele Sgroi.\n
LOCATION:https://researchseminars.org/talk/BUGeom/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephan Stolz (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20211027T200000Z
DTEND;VALUE=DATE-TIME:20211027T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/31
DESCRIPTION:Title:
TMF-cohomology via 2-dimensional QFTs\nby Stephan Stolz (University of
Notre Dame) as part of Boston University Geometry/Physics Seminar\n\nLect
ure held in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nTopological modul
ar form theory is a generalized cohomology theory whose coefficient ring T
MF^*(point) is rationally isomorphic to the ring of integral modular forms
. Modular forms also show up as partition functions of suitable 2-dimensio
nal QFTs. For example\, the Witten genus W(X) of a closed manifold X is an
integral modular form\, provided X is a spin manifold and the first Pontr
yagin class of X is trivial. This led to the question whether the correspo
nding spectrum TMF can be constructed in terms of 2D field theories. \n\n
\nIn this talk I will recall a result of Teichner and myself according to
which the partition function of a supersymmetric 2D Euclidean field theory
is an integral modular form\, as well as a Conjecture expressing the spac
es which form the spectrum TMF as spaces of supersymmetric 2D field theori
es.\n
LOCATION:https://researchseminars.org/talk/BUGeom/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Doran (University of Alberta)
DTSTART;VALUE=DATE-TIME:20211110T210000Z
DTEND;VALUE=DATE-TIME:20211110T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/32
DESCRIPTION:Title:
The Greene-Plesser Construction Revisited\nby Charles Doran (Universit
y of Alberta) as part of Boston University Geometry/Physics Seminar\n\nLec
ture held in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nThe first known
construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesse
r “quotient and resolve” procedure which applies to pencils of hypersu
rfaces in projective space. We’ll review this approach\, uncover the hi
nts it gives for some more general mirror constructions\, and describe a b
rand-new variant that applies to pencils of hypersurfaces in Grassmannians
. This last is joint work with Tom Coates and Elana Kalashnikov (arXiv:21
10.0727).\n
LOCATION:https://researchseminars.org/talk/BUGeom/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Cliff (University of Sherbrooke)
DTSTART;VALUE=DATE-TIME:20211201T210000Z
DTEND;VALUE=DATE-TIME:20211201T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/33
DESCRIPTION:Title:
Moduli spaces of principal 2-group bundles and a categorification of the F
reed--Quinn line bundle\nby Emily Cliff (University of Sherbrooke) as
part of Boston University Geometry/Physics Seminar\n\nLecture held in Zoom
meeting ID: 953 4652 9200.\n\nAbstract\nA 2-group is a higher categorical
analogue of a group\, while a smooth 2-group is a higher categorical anal
ogue of a Lie group. An important example is the string 2-group\, defined
by Schommer-Pries. We study the notion of principal bundles for smooth 2-g
roups\, and investigate the moduli "space" of such objects. \n\n\n\nIn par
ticular in the case of flat principal bundles for a finite 2-group over a
Riemann surface\, we prove that the moduli space gives a categorification
of the Freed--Quinn line bundle. This line bundle has as its global sectio
ns the state space of Chern--Simons theory for the underlying finite group
. We can also use our results to better understand the notion of geometric
string structures (as previously studied by Waldorf and Stolz--Teichner).
\n
LOCATION:https://researchseminars.org/talk/BUGeom/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengping Gui (ITCP)
DTSTART;VALUE=DATE-TIME:20220209T210000Z
DTEND;VALUE=DATE-TIME:20220209T220000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/34
DESCRIPTION:Title:
Elliptic trace map on chiral algebras\nby Zhengping Gui (ITCP) as part
of Boston University Geometry/Physics Seminar\n\nLecture held in Zoom mee
ting ID: 953 4652 9200.\n\nAbstract\nTrace map on deformation quantized al
gebra leads to the\nalgebraic index theorem. We investigate a two dimensio
nal chiral analogue\nof the algebraic index theorem via the theory of chir
al algebras developed\nby Beilinson and Drinfeld. We construct a trace map
on the elliptic chiral\nhomology of the free beta-gamma system using the
BV\nquantization framework. As an example\, we compute the trace evaluated
on\nthe unit constant chiral chain and obtain the formal Witten genus in
the\nLie algebra cohomology.\nThis talk is based on joint work with Si Li.
\n
LOCATION:https://researchseminars.org/talk/BUGeom/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Costello (Perimeter Institute)
DTSTART;VALUE=DATE-TIME:20220330T200000Z
DTEND;VALUE=DATE-TIME:20220330T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/35
DESCRIPTION:Title:
Amplitudes as vertex algebra correlators\nby Kevin Costello (Perimeter
Institute) as part of Boston University Geometry/Physics Seminar\n\nLectu
re held in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nI will talk about
joint work with Natalie Paquette\, which demonstrates how certain scatteri
ng amplitudes of a 4 dimensional gauge theory can be computed as correlati
on functions of a vertex algebra. This will be aimed at a mathematical au
dience\, and I will attempt to define any unfamiliar concepts.\n
LOCATION:https://researchseminars.org/talk/BUGeom/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Linshaw (University of Denver)
DTSTART;VALUE=DATE-TIME:20220413T200000Z
DTEND;VALUE=DATE-TIME:20220413T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/36
DESCRIPTION:Title:
Global sections of the chiral de Rham complex for Calabi-Yau and hyperkahl
er manifolds\nby Andrew Linshaw (University of Denver) as part of Bost
on University Geometry/Physics Seminar\n\nLecture held in Zoom meeting ID:
953 4652 9200.\n\nAbstract\nFor any complex manifold M\, the chiral de Rh
am complex is a sheaf of vertex algebras on M that was introduced in 1998
by Malikov\, Schechtman\, and Vaintrob. It is N-graded by conformal weight
\, and the weight zero piece coincides with the ordinary de Rham sheaf. Wh
en M is a Calabi-Yau manifold with holonomy group SU(d)\, it was shown by
Ekstrand\, Heluani\, Kallen and Zabzine that the algebra of global section
s \\Omega^{ch}(M) contains a certain vertex algebra defined by Odake which
is an extension of the N=2 superconformal algebra. When M is a hyperkahle
r manifold\, it was shown by Ben-Zvi\, Heluani\, and Szczesny that \\Omega
^{ch}(M) contains the small N=4 superconformal algebra. In this talk\, we
will show that in both cases\, these subalgebras are actually the full alg
ebras of global sections. In an earlier work\, Bailin Song has shown that
the global section algebra can be identified with a certain subalgebra of
a free field algebra which is invariant under the action of an infinite-di
mensional Lie algebra of Cartan type. The key observation is that this alg
ebra can be described using the arc space analogue of Weyl's first and sec
ond fundamental theorems of invariant theory for the special linear and sy
mplectic groups. \n\n \n\nThis is a joint work with Bailin Song.\n
LOCATION:https://researchseminars.org/talk/BUGeom/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nate Bottman (Max-Planck Institute)
DTSTART;VALUE=DATE-TIME:20220504T200000Z
DTEND;VALUE=DATE-TIME:20220504T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/37
DESCRIPTION:Title:
The Barr--Beck theorem in symplectic geometry\nby Nate Bottman (Max-Pl
anck Institute) as part of Boston University Geometry/Physics Seminar\n\nL
ecture held in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nThe Barr--Beck
theorem gives conditions under which an adjunction F -| G is monadic. Mon
adicity\, in turn\, means that the category on the right can be computed i
n terms of the data of the category on the left and its endomorphism GF. I
will present joint work-in-progress with Abouzaid\, in which we consider
this theorem in the case of the functors between Fuk(M1) and Fuk(M2) assoc
iated to a Lagrangian correspondence L12 and its transpose. These functors
are often adjoint\, and under the hypothesis that a certain map to symple
ctic cohomology hits the unit\, the hypotheses of Barr--Beck are satisfied
. This can be interpreted as an extension of Abouzaid's generation criteri
on\, and we hope that it will be a useful tool in the computation of Fukay
a categories.\n
LOCATION:https://researchseminars.org/talk/BUGeom/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurbir Dhillon (Yale University)
DTSTART;VALUE=DATE-TIME:20220914T200000Z
DTEND;VALUE=DATE-TIME:20220914T210000Z
DTSTAMP;VALUE=DATE-TIME:20230926T001815Z
UID:BUGeom/38
DESCRIPTION:Title:
The log Kazhdan--Lusztig correspondence\nby Gurbir Dhillon (Yale Unive
rsity) as part of Boston University Geometry/Physics Seminar\n\nLecture he
ld in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nA landmark discovery of
the 1980s\, due to many mathematicians and\nphysicists (Drinfeld\, Kohno\
, Witten\, etc.)\, was the close relationship between quantum groups and a
ffine Lie algebras. Kazhdan–Lusztig established a sharp form of\nthis in
representation theory via an equivalence of braided tensor categories of
modules. The subtlest cases of their result occur when the quantum paramet
er q is\na root of unity\, where one has to pick the right form of the qua
ntum group (the\nso-called Lusztig\, or divided-powers form) in order for
the equivalence to hold. In\nthe mid-2000s\, Feigin–Gainutdinov–Semikh
atov–Tipunin conjectured a similar ‘log\nKazhdan–Lusztig corresponde
nce’ between representations of another version of the\nquantum group\,
the small quantum group\, and a vertex algebra known as the triplet\,\nat
certain roots of unity. After providing a survey of these influential work
s for nonspecialists\, we will propose a conjecture extending that of Feig
in et. al. to all roots\nof unity. Time permitting\, we will indicate a wa
y to prove it conditional on some\nfoundational conjectures in quantum geo
metric Langlands.\n
LOCATION:https://researchseminars.org/talk/BUGeom/38/
END:VEVENT
END:VCALENDAR