The SGGTC seminar meets on Fridays in Math 407 at 1pm, unless noted otherwise (in red).

Previous semesters: Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007.

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SGGTC Seminar Schedule

Sep. 9 11am
Math 622
Eugene Gorsky
(UC Davis)
Khovanov-Rozansky homology and the flag Hilbert scheme
Sep. 16
Heather Lee
Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions
Sep. 23
Rob Silversmith
(University of Michigan)
A mirror theorem for symmetric products of projective space
Sep. 30
Michael Willis
(University of Virginia)
A Colored Khovanov Homotopy Type
Oct. 7
Cheuk Yu Mak
Symplectic log Calabi-Yau surfaces
Oct. 14
Peter Koroteev
(University of Minnesota)
Non-commutative instantons from large-n limit of Seiberg-Witten theories
Oct. 21
Andrew Lee
(University of Texas at Austin)
Surface Bundles and Stable Pairs
Oct. 28
Ian Zemke
Link cobordisms and functoriality in link Floer homology
Nov. 4
Jake Solomon
(Hebrew University of Jerusalem / IAS)
Nov. 4 2:10pm
Math 520
C.-M. Michael Wong
(Columbia University)
Nov. 7-11 Workshop on Homological Mirror Symmetry (at IAS)
Nov. 18
Yu-Shen Lin
(Columbia University)
Nov. 25
Dec. 2
Oleg Lazarev
(Stanford University)
Dec. 9
Hülya Argüz (IAS)
Mark McLean (Stony Brook)
Luis Diogo (Columbia University)



September 9, 2016: Eugene Gorsky "Khovanov-Rozansky homology and the flag Hilbert scheme"

Abstract: The Jucys-Murphy elements are known to generate a maximal commutative subalgebra in the Hecke algebra. They can be categorified to a family of commuting complexes of Soergel bimodules. I will describe a relation between a category generated by these complexes and the category of sheaves on the flag Hilbert scheme of points on the plane, using the recent work of Elias and Hogancamp on categorical diagonalization. As an application, I will give an explicit conjectural description of the Khovanov-Rozansky homology of generalized torus links. The talk is based on a joint work with Andrei Negut and Jacob Rasmussen.

September 16, 2016: Heather Lee "Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions"

Abstract: We will demonstrate one direction of HMS for punctured Riemann surfaces - the wrapped Fukaya category of a punctured Riemann surface is equivalent to the matrix factorization category MF(X,W) of the toric Landau-Ginzburg mirror (X, W). The category MF(X,W) can be constructed from a Cech cover of (X,W) by local affine pieces that are mirrors of pairs of pants. We supply a suitable model for the wrapped Fukaya category for a punctured Rimemann surface so that it can also be explicitly computed in a sheaf-theoretic way, from the wrapped Fukaya categories of various pairs of pants in a decomposition. The pieces are glued together in the sense that the restrictions of the wrapped Floer complexes from two adjacent pairs of pants to their adjoining cylindrical piece agree.

September 23, 2016:Rob Silversmith "A mirror theorem for symmetric products of projective space"

Abstract: Through 3 general points and 6 general lines in $\mathbb P^3$, there are exactly 190 twisted cubics; 190 is a Gromov-Witten invariant of $\mathbb P^3$. Mirror symmetry is a beautiful conjecture about the structure of all Gromov-Witten invariants of a smooth variety (or orbifold) X. It is also an important step towards solving many interesting and difficult problems, such as Ruan's Crepant Resolution Conjecture, relating the Gromov-Witten invariants of an orbifold to those of a crepant resolution. One of the prime examples of a crepant resolution is the resolution of $Sym^d(\mathbb P^2)$ by the Hilbert scheme of points — this was one of Ruan’s motivating examples. However, mirror symmetry has proved difficult in this case; it is essentially known only for toric orbifolds and some of their complete intersections (after much difficult work). We prove the mirror theorem for $Sym^d(\mathbb P^r)$, and on the way we develop techniques for dealing with nonabelian orbifolds.

September 30, 2016: Michael Willis "A Colored Khovanov Homotopy Type"

Abstract: I will use cablings with infinite torus braids to define a Khovanov homotopy type for $sl_2(C)$ colored links and discuss some of its basic properties. In the case of n-colored B-adequate links, I will describe a stabilization of the homotopy types as the coloring n goes to infinity, generalizing the tail behavior of the colored Jones polynomial. In the case of the unknot, I will also describe a simpler argument for stabilization. If time permits, I will also discuss a more recent result regarding stabilization involving more general infinite braids.

October 7, 2016: Cheuk Yu Mak "Symplectic log Calabi-Yau surfaces"

Abstract: In this talk, we introduce a symplectic analogue of log Calabi Yau surfaces and classify them up to symplectic deformation equivalence.

October 14, 2016: Peter Koroteev "Non-commutative instantons from large-n limit of Seiberg-Witten theories"

Abstract: We study moduli space of U(n) instantons with ramification (rank-n torsion free sheaves on P^2 with framing at infinity). It can be argued that the instanton partition function (holomorphic equivariant Euler characteristic) satisfies a system of differential or difference equations which coincide with energy equation for some integrable n-body system of Calogero-Moser or Ruijsenaars type. We then take a limit, when the number of particles becomes large, and recover a different effective integrable model — intermediate long wave hydrodynamics. Spectrum of this model describes quantum multiplication in the small cohomology ring of the moduli space of non-commutative instantons on C^2 and ALE spaces. We shall formulate some results and conjectures on related topics.

October 21, 2016: Andrew Lee "Surface Bundles and Stable Pairs"

Abstract: In this talk we use a construction of a moduli space of stable pairs over a Riemann surface to produce a Floer-theoretic invariant of a surface bundle over the circle (together with a choice of line bundle on it). We then outline a calculation of this invariant for a certain class of torus bundles. This is joint work with Tim Perutz.

October 28, 2016: Ian Zemke " Link cobordisms and functoriality in link Floer homology"

Abstract: In this talk we'll describe an approach to defining cobordism maps in link Floer homology for decorated link cobordisms. We'll describe the maps which feature in the construction, and describe some of the steps to proving invariance. We'll describe some basic properties of the maps, such as a grading change formula. We'll describe several applications of the theory, such as a proof of the formula for the ``Sarkar map'', and quick proofs of several well known bounds on the concordance invariant tau.

Our e-mail list.

Announcements for this seminar, as well as for related seminars and events, are sent to the "Floer Homology" e-mail list maintained via Google Groups.