The SGGTC seminar meets on Fridays in Math 417, at 10:45 am unless noted otherwise (in red).
Previous semesters: Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007.
Future semesters: Spring 2012
Other area seminars and conferences. Our email list.
(iCal)
Date  Speaker  Title 
Sep 9 10:45 am 
CheolHyun Cho Seoul National University/ Northwestern University 
Lagrangian Floer cohomology for toric orbifolds 
Sep 9 1:20 pm Math 520 
Organizational Meeting 
Organizational Meeting Joint with Geometric Topology Seminar 
Sep 16  No seminar this week 

Sep 23  Nicolo Sibilla Northwestern University 
Mirror Symmetry and Ribbon Graphs 
Sep 30  Anthony Licata IAS/Australian National University 
Affine Lie algebras, Hilbert schemes and Categorification 
Oct 7  Egor Shelukhin Tel Aviv University 
Action homomorphisms, moment maps and quasimorphisms 
Oct 14  Maksim Lipyanskiy Columbia University 
GromovUhlenbeck Compactness 
Oct 21 
Emmanuel Wagner Institut Mathématique de Bourgogne 
Alexander polynomial and enhanced Kauffman states 
Oct 21 10:45 am 
Sobhan Seyfaddini UC Berkeley 
C^0 limits of Hamiltonian paths and spectral invariants 
Oct 28  Anton Zeitlin Yale University 
LianZuckerman homotopy algebras, Courant/Vertex algebroids and betafunctions of string theory 
Nov 4 10:45 am 
Florent Schaffhauser University of Los Andes 
YangMills equations over Klein surfaces 
Nov 4 3:30 pm Math 507 
Raphael Rouquier UCLA 
KazhdanLusztig theory and CalogeroMoser spaces 
Nov 11  Steven Sivek Harvard University 
Monopole Floer homology and Legendrian knots 
Nov 18  Rumen Zarev UC Berkeley 
Toward a minus version of bordered Heegaard Floer homology 
Nov 25  No seminar this week  
Dec 1 2:00 pm Math 622 
Dustin Ross Colorado State University 
Open GW Theory and the Orbifold Vertex 
Dec 2  Yang Huang USC 
An absolute grading of Heegaard Floer homology by homotopy classes of 2plane fields 
Dec 9  John Baldwin Princeton University 
The equivalence of transverse link invariants in knot Floer homology 
Dec 16 
Nick Sheridan MIT 
Homological Mirror Symmetry for a CalabiYau hypersurface in projective space 
Dec 16 10:45 am 
Eugene Gorski Stony Brook University 
A model for the stable Khovanov homology of torus knots 
Abstracts
September 9, 2011
CheolHyun Cho, "Lagrangian Floer cohomology for toric orbifolds"
Abstract: Floer cohomology for Lagrangian torus fibers in toric manifolds has been extensively studied in the last decade. We discuss an analogous theory for toric orbifolds by studying holomorphic orbifold discs. We classify such orbidiscs in Fano toric orbifolds, compute Floer cohomology and discuss nondisplaceability of Lagrangian torus fibers in these cases.
September 23, 2011
Nicolo Sibilla, "Mirror Symmetry and Ribbon Graphs"
Abstract: In this talk, I will explain how to construct a model for the Fukaya category of punctured Riemann surfaces in terms of a sheaf of dgcategories over a suitable category of ribbon graphs. Using this model, I will be able to prove a homological mirror symmetry statement for degenerate ellitpic curves. This is joint with Treumann and Zaslow. If time permits, I will also discuss recent work of myself on mapping class group actions on derived categories of coherent sheaves, which is motivated by the above mirror symmetry framework.
September 30, 2011
Anthony Licata, "Affine Lie algebras, Hilbert schemes and Categorification"
Abstract: The basic representation of a simplylaced affine KacMoody Lie algebra was constructed by FrenkelKac and Segal using "vertex operators". We describe a categorification of this construction and explain how this categorification appears in the geometry of Hilbert schemes of points on the resolution of a simple singularity. (Joint with Sabin Cautis)
October 7, 2011
Egor Shelukhin, "Action homomorphisms, moment maps and quasimorphisms"
Abstract: Whenever a group acts on a symplectic space with an equivariant moment map, an analogue of Weinstein's action homomorphism can be defined. If there is also an invariant system of 'geodesic' paths, such that the corresponding geodesic triangles have uniformly bounded symplectic areas, we define a quasimorphism on the universal cover of the group. This applies to the action of the Hamiltonian group on the space of compatible almost complex structures (with the moment map of Donaldson and Fujiki) producing a nontrivial quasimorphism on the universal cover of Ham for every symplectic manifold of finite volume. We discuss this construction, some additional properties and applications.
October 14, 2011
Maksim Lipyanskiy, "GromovUhlenbeck Compactness"
Abstract: We introduce an analytic framework that, in special circumstances, unites YangMills theory and the theory of pseudoholomorphic curves. As an application of these ideas, we discuss the relation between the categorification of the Casson invariant based on gauge theory and symplectic geometry.
October 21, 2011, 9:30 a.m.
Emmanuel Wagner, "Alexander polynomial and enhanced Kauffman states"
Abstract: State sum formulas play a key role in quantum topology, and are even more relevant for the new purpose of categorification. Among polynomial link invariants, the two most popular are probably the Alexander polynomial and the Jones polynomial. The Jones polynomial has a natural state sum formula in terms of so called enhanced Kauffman states. In this talk, we will see that the set of enhanced Kauffman states can also be used as a set of states for a formula for the Alexander polynomial.
October 21, 2011, 10:45 a.m.
Sobhan Seyfaddini, "C^0 limits of Hamiltonian paths and spectral invariants"
Abstract: After briefly reviewing spectral invariants, I will write down an estimate, which under certain assumptions, relates the spectral invariants of a Hamiltonian to the C^0distance of its flow from the identity. I will also show that, unlike the Hofer norm, the spectral norm is C^0continuous on surfaces. Time permitting, I will present an application to the study of area preserving disk maps.
October 28, 2011
Anton Zeitlin, "LianZuckerman homotopy algebras, Courant/Vertex algebroids and betafunctions of string theory"
Abstract: Homotopy algebras of Lian and Zuckerman for topological vertex operator algebras (TVOA) will be discussed. In a paticular case of semiinfinite complex of Virasoro algebra, it appears that the corresponding MaurerCartan equations reproduce betafunctions of sigma models for certain VOA, i.e. YangMills and Einstein equations with stringy corrections. As a byproduct this leads to a surprising relation between Courant algebroids and classical field equations.
November 4, 2011, 10:45 a.m.
Florent Schaffhauser, "YangMills equations over Klein surfaces"
Abstract: Moduli spaces of semistable algebraic vector bundles on a real algebraic curve / Klein surface can be constructed using a gaugetheoretic approach, in which they are viewed as spaces of solutions to YangMills equations over a compact Riemann surface, satisfying an additional Galois symmetry. From the symplectic point of view, these moduli spaces are Lagrangian quotients, defined by means of an involution on the space of all unitary connections on a fixed Hermitian bundle. By adapting the equivariant approach of Atiyah and Bott to a setting with involutions, we compute the mod 2 Poincare polynomial of these Lagrangian quotients. This is joint work with ChiuChu Melissa Liu.
November 4, 2011, 3:30 p.m.
Raphael Rouquier, "KazhdanLusztig theory and CalogeroMoser spaces"
Abstract: Rational double affine Hecke algebras are related to finitedimensional Hecke algebras via monodromy representations. By degenerating both sides, one expects a relation between CalogeroMoser spaces and Lusztig's asymptotic ring. We will explain a conjectural construction of left cells in Weyl groups in terms of ramification for CalogeroMoser spaces. (joint work with Cedric Bonnafe)
November 11, 2011, 10:45 a.m.
Steven Sivek, "Monopole Floer homology and Legendrian knots"
Abstract: We will define invariants of Legendrian knots using Kronheimer and Mrowka's construction of monopole Floer homology for sutured manifolds. We will discuss several interesting properties of these invariants, including behavior under stabilization and contact surgery which suggests that they are closely related to the LiscaOzsvathStipsiczSzabo invariant in knot Floer homology, and show that they are functorial with respect to Lagrangian concordance.
November 18, 2011, 10:45 a.m.
Rumen Zarev, "Toward a minus version of bordered Heegaard Floer homology"
Abstract: Bordered Heegaard Floer homology, in its current state, can recover the hat version of Heegaard Floer homology for closed manifolds. It is related to the sutured Floer homology, and gluing sutured manifolds along surfaces with boundary. One idea for expanding the bordered framework to obtain the stronger plus/minus versions of HF, is to look at sutured manifolds and gluing along closed boundary components. I will discuss progress along this lines, as well as connections to other possible approaches.
December 1, 2011, 2:00 p.m.
Dustin Ross, "Open GW Theory and the Orbifold Vertex"
Abstract: Almost 10 years ago, Aganagic, Klemm, Marino, and Vafa proposed the topological vertex, a basic building block for GromovWitten theory in all genera of toric CalabiYau 3folds. The topological vertex has now been realized in a number of equivalent ways: via Schur functions, 3d partitions with prescribed asymptotics, and threepartition Hodge integrals on the moduli space of curves. The orbifoldvertex is the natural extension of the topological vertex to toric orbifold targets. I will discuss recent work in which the orbifold vertex is realized as a generating function of open orbifold GW invariants of the orbifold [C^3/G], defined by generalizing the open invariants of Katz and Liu. I will also discuss the conjectural correspondence with the DT orbifold vertex developed by BryanCadmanYoung.
December 2, 2011, 10:45 a.m.
Yang Huang, "An absolute grading of Heegaard Floer homology by homotopy classes of 2plane fields"
Abstract: In 2001, P. Ozsvath and Z. Szabo introduced Heegaard Floer homology, which is an invariant of closed, oriented 3manifolds. The Heegaard Floer homology group splits into a direct sum according to Spin^c structures. Each direct summand is relatively graded by Z mod d where d is the divisibility of the first Chern class of the Spin^c structure. In this talk we discuss an absolute grading of Heegaard Floer homology by homotopy classes of 2plane fields in a 3manifold. In particular we define an absolute Qgrading for torsion Spin^c structures which coincides with the one defined by OzsvathSzabo. This is joint work with Vinicius Gripp.
December 9, 2011, 10:45 a.m.
John Baldwin, "The equivalence of transverse link invariants in knot Floer homology"
Abstract: Using the grid diagram formulation of knot Floer homology, Ozsvath, Szabo and Thurston dened an invariant of transverse knots in the tight contact 3sphere. A bit later, Lisca, Ozsvath, Stipsicz and Szabo defined an invariant of transverse knots in arbitrary contact 3manifolds using open book decompositions. It has been conjectured that these invariants agree where they overlap. I'll discuss a proof of this conjecture. Our strategy is to define yet another invariant of transverse knots and show that this third invariant agrees with the two invariants mentioned above. This is joint work with Vera Vertesi and David Shea VelaVick.
December 16, 2011, 9:30 a.m.
Nick Sheridan, "Homological Mirror Symmetry for a CalabiYau hypersurface in projective space"
Abstract: We prove homological mirror symmetry for a smooth CalabiYau hypersurface in projective space. In the onedimensional case, this is the elliptic curve, and our result is related to that of PolishchukZaslow; in the twodimensional case, it is the K3 quartic surface, and our result reproduces that of Seidel; and in the threedimensional case, it is the quintic threefold (also considered by NoharaUeda, using our work). After stating the result carefully, we will describe some of the techniques used in its proof, and draw pictures in the onedimensional case.
December 16, 2011, 10:45 a.m.
Eugene Gorsky, "A model for the stable Khovanov homology of torus knots"
Abstract: In 2005 S. Gukov, N. Dunfield and J. Rasmussen conjectured that the Khovanov homology of some knots can be computed by taking the homology of a certain differential acting on triply graded homology of a knot. They also conjectured the simple description of the stable limit of the triply graded homology for (n,m) torus knots when m is large. I will discuss the conjectural algebraic description of the differential and its homology that matches all known experimental data. When both m and n tend to infinity, the Poincare series for the homology turns out to be related to the RogersRamanujan identity. The talk is based on a joint work with A. Oblomkov and J. Rasmussen.
Other relevant information
Conferences
 Workshop on Equivariant Quantum Differential Equations
Columbia University
September 16 – 19, 2011
 Workshop on Symplectic Dynamics
Institute for Advanced Study
October 10 – 14, 2011
Other area seminars
 Columbia Geometric Topology Seminar
 Columbia Algebraic Geometry Seminar
 Eilenberg
lecture series at Columbia:
Benedict Gross on "Representation theory and number theory"  Princeton Topology Seminar
 IASPrinceton Symplectic Geometry Seminar
Our email list.
Announcements for this seminar, as well as for related seminars and events, are sent to the "Floer Homology" email list maintained via Google Groups. You can subscribe directly via Google Groups or by contacting R. Lipshitz.