Organized by Lev Borisov,
Diuliu Diaconescu, and Chris Woodward
Thursday, 9/24, Rahul Pandharipande, Princeton in SEC 218.
Title: Quivers, curves, and symplectomorphisms of the algebraic 2-torus.
Abs. I will talk about the relationship between Euler chars
of moduli\\ spaces of quivers, curve counts on toric surfaces, and
commutators in the symplectomorphism group of the algebraic 2-torus.
I will cover results of Reineke, Gross-Siebert, and others.
(Joint with String Group Meeting)
Friday, 10/2 Lev Borisov, Rutgers, 11:45 in Hill 425
"In search of families of dg-algebras related to resolutions of
Gorenstein toric singularities"
Abstract: A Gorenstein toric singularity can be described by simple
combinatorial data, namely a convex polytope $P$ in ${bf Z}^n$ with
integer vertices. Different triangulations of $P$ with vertices given
by integer points of $P$ give rise to different resolutions of the
singularity. It has been shown that bounded derived categories of
coherent sheaves on these resolutions are equivalent. It is reasonable
to expect that there is in fact a continuous family of triangulated
categories that includes these categories as its limit points. This is
very much work in progress, and the main questions are still wide
open. It is my hope that by bringing this problem to your attention I
can inspire someone to find such construction.
(Joint with quantum math/ Lie theory/algebra)
Thursday, 10/8 Katrin Wehrheim, MIT, 1:30pm in SEC 218.
Calculations of Floer homology by reduction":
I will give some examples of calculating monotone Floer homology from a
general strip shrinking isomorphism in quilted Floer homology (for
sequences of Lagrangian correspondences). Examples include the
Clifford torus in CP^n (previously known by Cho) and nondisplaceable
T^{n-k}\times S^{2k-1} in CP^n\times CP^{k-1}. Moreover, the bijection
of trajectory moduli spaces can be somewhat generalized to multiply
covered compositions of correspondences, yielding e.g. calculations of
the Floer homology between Clifford tori and RP^n in CP^n (confirming
work by Allston). Finally, "figure eight" bubbling obstructions can be
understood explicitly. Work is in progress on overcoming these for the
Chekanov/Polterovich torus in S^2\times S^2; using symmetries and
twisted coefficients.
Thursday, 10/15 Emanuel Diaconescu, Rutgers
Title: ADHM sheaves, wallcrossing and local stable pair invariants
Abstract: The local stable pair theory of a curve will be constructed
in terms of ADHM sheaves satisfying ceratin stability
conditions. Wallcrossing formulas for the resulting invariants will be
derived, and applications to local Gopakumar-Vafa theory will also be
presented,
Thursday, 10/22 Yaron Ostrover, IAS
Title: Algebraic properties of the quantum homology.
Abstract: In this talk we discuss certain algebraic properties of the
quantum homology algebra of toric Fano manifolds. In particular, we
describe an easily-verified sufficient condition for the
semi-simplicity of the quantum homology. (This is a joint work with
Ilya Tyomkin.)
Thursday, 10/29 Ron Donagi, U Penn
Approx title: F-theory and its compactifications
Abstract: F-theory is a "12 dimensional variant of string theory"
whose study has seen great progress in the past year or two. This will
be an introduction for mathematicians to F-theory and its global and
local compactifications, including some of the recent progress towards
F-theory based phenomenology. I will discuss the issue of local versus
global in F-theory (and strings), and explore connections to the
geometry of del Pezzo surfaces, Higgs bundles, and Noether-Lefschetz
loci.
Thursday, 11/5 Bohan Fang, Northwestern
Title: Coherent-constructible correspondence for toric varieties and
stacks
Abstract: This is a talk on joint works with Chiu-Chu Liu, David
Treumann and Eric Zaslow. I will describe a coherent-constructible
correspondence for toric varieties motivated by homological mirror
symmetry and T-duality. To each ample line bundle one can assign a
polytope-shaped constructible sheaf on a real vector space. This
assignment turns out to be a tensorial quasi-equivalence. The
correspondence can be extended to toric stacks, using
Borisov-Chen-Smith's definition through stacky fans.
Thursday, 11/12 Davesh Maulik, MIT
Title: Gromov-Witten theory of K3 surfaces
Abstract: In this talk, we will survey some recent progress in
understanding the Gromov-Witten theory of K3 surfaces. In particular, we
will prove and exploit relations with sheaf theory to prove some old
conjectures in the subject (joint with R. Pandharipande and R. Thomas)
Thursday, 11/19 no seminar
Thursday, 11/26 no seminar (Thanksgiving)
Thursday, 12/3 no seminar
Thursday 12/10 Chris Woodward, Rutgers
Title: Gauged Gromov-Witten theory and the mirror map
Abstract: I will explain how mirror theorems of Givental etc. are a special
case of "quantum non-abelian localization" relating the Gromov-Witten
invariants of a symplectic quotient with the gauged Gromov-Witten
invariants of the action. In particular, the "mirror map" is
generalized to a "morphism of CohFT"s which counts "affine vortices".
Applications to abelianization conjecture of Hori-Vafa,
Bertam-Ciocan-Fontanine-Kim etc. will be discussed. This is joint
in progress with Ziltener, Gonzalez, Ott, and Venugopalan.
Thursday 12/10 Lev Borisov, Rutgers
Tuesday, 2/9 Melissa Liu, Columbia
Thursday, 2/??? Mohammed Abouzaid, MIT
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