The SGGTC seminar meets on Fridays in Math 417, at 10:45 am unless noted otherwise.
Next semester: Spring 2011
Previous semesters: Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007.
Other area seminars. Our email list.
Special Event: Columbia will host Categorification on Broadway, a graduate student Workshop on Tuesday, December 14 and Wednesday, December 15.
Date  Speaker  Title 
Sep 10 1:15 pm 
Organizational Meeting Unusual time this week only: 1:15 pm. 

Sep 17  Ben Elias (Columbia) 
A diagrammatic categorification of the Hecke algebra 
Sep 24  Adam Knapp (Columbia) 
Monopoles, cobordisms, and exact triangles 
Oct 1  Florent Schaffhauser (University of Los Andes) 
Moduli of real and quaternionic bundles over a curve 
Oct 8  Adam Levine (Brandeis) 
Twisted coefficients and the unoriented skein sequence for HFK 
Oct 15  Yiqiang Li (Virginia Tech) 
Geometric realizations of quantum groups 
Oct 22  Sikimeti Ma'u (Columbia) 
Quilts and Ainfinity structures 
Oct 29  Michael Usher (University of Georgia) 
Deformed Hamiltonian Floer theory and Calabi quasimorphisms 
Nov 5  Allison Gilmore (Columbia) 
An algebraic proof of invariance for knot Floer homology 
Note: There are two talks on November 12!  
Nov 12 9:30 am 
Cagatay Kutluhan (Columbia) 
Heegaard Floer meets SeibergWitten 
Nov 12 10:45 am 
Jeremy Van HornMorris (American Institute of Mathematics) 
Spinal open book decompositions and symplectic fillings 
Nov 19  Eamonn Tweedy (UCLA) 
On the antidiagonal filtration for the Heegaard Floer chain complex of a branched doublecover 
MONDAY Nov 22 4:00 pm Math 507 
Matthew Hogancamp (UVA) 
SO(3) Kauffman Homology for Graphs and Links 
TUESDAY Nov 30 4:45 pm Math 507 
Richard Hind (Notre Dame) 
Symplectic embeddings of polydisks 
WEDNESDAY Dec 1 4:10 pm  5:00 pm Math 507 
Matthew Borman (University of Chicago) 
Symplectic Reduction of Quasimorphisms and Quasistates 
MONDAY Dec 6 4:00 pm 
Noboru Ito (Waseda University) 
A colored Khovanov bicomplex 
Note: There are two talks on December 10!  
Dec 10 9:30 am 
Andrew CottonClay (Harvard) 
Holomorphic Pairs of Pants in Mapping Tori 
Dec 10 10:45 am 
Timothy Nguyen (MIT) 
The SeibergWitten Equations on Manifolds with Boundary 
Dec 17 Math 307 
Ben Mares (McMaster University) 
Some analytic aspects of VafaWitten twisted N=4 supersymmetric YangMills theory 
Abstracts
September 10, 2010
Organizational Meeting
Unusual time this week only: 1:15 pm.
September 17, 2010
Ben Elias, "A diagrammatic categorification of the Hecke algebra"
Abstract: The Hecke algebra in Type A is a ubiquitous algebra in representation theory, knot theory, and geometry. Soergel provided a simple and easytouse categorification of the Hecke algebra, using bimodules over a polynomial ring. We explain this categorification, and briefly motivate it in the context of equivariant cohomology of flag varieties. Then, we give an even simpler version of the same categorification, using planar graphs to represent morphisms in Soergel's category (joint work w/ M. Khovanov). Finally, we will discuss applications to knot theory, including the functoriality of KhovanovRozansky link homology (joint work w/ D. Krasner).
September 24, 2010
Adam Knapp, "Monopoles, cobordisms, and exact triangles"
Abstract: Suppose W_0 is a cobordism between two 3manifolds Y and Y_0. When Y_0 is a member of a certain class of surgery exact triangle (with 3manifolds Y_0, Y_1, and Y_2), I provide a method of computing the map on Monopole Floer homology induced by W_0 in terms of the maps induced by cobordisms W_1 and W_2 from Y to Y_1 and Y_2 respectively.
October 1, 2010
Florent Schaffhauser, "Moduli of real and quaternionic bundles over a curve"
Abstract: We examine the moduli problem for real and quaternionic vector bundles over a curve, and we give a gaugetheoretic construction of moduli varieties for such bundles. These moduli varieties are irreducible subsets of real points inside a complex projective variety. We relate our point of view to previous work by Biswas, Huisman and Hurtubise, and we use this to study the induced $Gal(C/R)$action on moduli varieties of semistable holomorphic bundles over a complex curve with given real structure $\sigma$. We show in particular a Harnacktype theorem, bounding the number of connected components of the fixedpoint set of that action by $2^g + 1$, where $g$ is the genus of the curve. We show, moreover, that any two such connected components are homeomorphic.
October 8, 2010
Adam Levine, "Twisted coefficients and the unoriented skein sequence for HFK"
Abstract: We shall describe some work in progress with John Baldwin concerning Manolescu's unoriented skein exact sequence for knot Floer homology. Under the right conditions, this sequence can be iterated to give a cube of resolutions that computes HFK. Using twisted coefficients in a Novikov ring greatly simplifies this cube complex, since the homology of any resolution with multiple components vanishes. It is hoped that this approach may yield a new way to compute HFK combinatorially and shed some light its possible relation to Khovanov homology and the Heegaard Floer homology of the double branched cover.
October 15, 2010
Speaker: Yiqiang Li, "Geometric realizations of quantum groups"
Abstract: I'll recall Beilinson, Lusztig and MacPherson's classical work on the geometric realization of quantum groups of type A by double partial flag varieties. Then I'll present my recent work on the geometric realization of quantum groups of symmetric type by using localized equivariant derived categories of double framed representation varieties associated with a quiver.
October 22, 2010
Sikimeti Ma'u, "Quilts and Ainfinity structures"
Abstract: I'll describe some Ainfinity structures associated to Lagrangians and Lagrangian correspondences, particularly Ainfinity modules, bimodules, and higher generalizations called nmodules. The structures can all be described pictorially in terms of quilted strips with markings, which are types of graph associahedra in disguise. The quilted strips are domains for holomorphic quilts (a la WehrheimWoodward), so they translate into Ainfinity structure on the target symplectic manifolds. So, for example, a sequence of Lagrangian correspondences between symplectic manifolds M and N determines a bimodule of the Fukaya categories of M and N. More generally there is an Ainfinity functor from Fuk(MxN) to Bimod(Fuk(M), Fuk(N)), which is really due to the underlying 3module.
October 29, 2010
Michael Usher, "Deformed Hamiltonian Floer theory and Calabi quasimorphisms"
Abstract: I'll introduce a family of deformations of the Hamiltonian Floer complex on a symplectic manifold which, on passing to homology, recover the "big" quantum homology of the manifold. Using these deformations, one can construct Calabi quasimorphisms on the universal covers of the Hamiltonian diffeomorphism groups of new families of symplectic manifolds, including all onepoint blowups.
November 5, 2010
Allison Gilmore, "An algebraic proof of invariance for knot Floer homology"
Abstract: We investigate the algebraic structure of knot Floer homology in the context of categorification. Ozsvath and Szabo gave the first completely algebraic description of knot Floer homology via a cube of resolutions construction. Starting with a braid diagram for a knot, one singularizes or smooths each crossing, then associates an algebra to each resulting singular braid. These can be arranged into a chain complex that computes knot Floer homology. Using this construction, we give a fully algebraic proof of invariance for knot Floer homology that avoids any mention of holomorphic disks or grid diagrams. We close with an alternative description of knot Floer homology in terms of Soergel bimodules that suggests a close relationship with HOMFLYPT homology.
November 12, 2010, 9:30 am
Cagatay Kutluhan, "Heegaard Floer meets SeibergWitten"
Abstract: Recently YiJen Lee, Clifford H. Taubes, and I have announced a proof of the conjectured equivalence between Heegaard Floer and SeibergWitten Floer homology groups of a closed, oriented 3manifold. In this talk, I will try to outline our construction of this equivalence.
November 12, 2010, 10:45 am
Jeremy Van HornMorris, "Spinal open book decompositions and symplectic fillings"
Abstract: Recently, C. Wendl used holomorphic curves to show that any strong filling of a planar open book comes as an extension of the open book to a Lefschetz fibration of the filling. I'll discuss a generalization of this result to spinal open books and discuss some applications, including a determination of fillability for contact structures on circle bundles. This is joint with S. Lisi and C. Wendl.
November 19, 2010
Eamonn Tweedy, "On the antidiagonal filtration for the Heegaard Floer chain complex of a branched doublecover"
Abstract: One can use a grading from Seidel and Smith's fixedpoint symplectic Khovanov cochain complex to obtain a filtration on the Heegaard Floerhat chain complex for the twofold cover of S^3 branched over a knot K (via an identification of generators). Although the definition comes from a braid whose closure is K, we in fact have that the resulting filtered chain homotopy type of the CFhat complex is a knot invariant (as are the higher pages of the spectral sequence induced by this filtration). Under certain spectral sequence degeneration conditions (satisfied by all twobridge knots, for instance), one obtains an absolute Maslov grading on HFhat of the branched doublecover. We'll outline the definitions, discuss invariance, give some results, and make some further speculations related to this filtration.
MONDAY, November 22, 2010, 4:00 pm in Math 507
Matt Hogancamp, "SO(3) Kauffman Homology for Graphs and Links"
Abstract: (Joint work with B. Cooper and S. Krushkal) There is a wellknown relationship between the SO(3) Kauffman polynomial for links, the chromatic polynomial for planar graphs, and the 2colored Jones polynomial. In this talk I will describe a categorification of this relationship using a categorified JonesWenzl projector on two strands, living in BarNatan's category. Some elementary properties will be discussed, as well as future directions.
TUESDAY, November 30, 2010, 4:45 pm in Math 507
Richard Hind, "Symplectic embeddings of polydisks"
Abstract: I will discuss some work in progress with Sam Lisi investigating obstructions to symplectically embedding fourdimensional polydisks into balls.
WEDNESDAY, December 1, 2010, 4:10 pm  5:00 pm
Matthew Borman, "Symplectic Reduction of Quasimorphisms and Quasistates"
Abstract: For certain complex hypersurfaces N in a Kahler manifold M, I will present a construction for symplectically reducing quasimorphisms on the universal cover of the Hamiltonian group of M to quasimorphisms on universal cover of the Hamiltonian group of N. Along the way I will show that spectral quasimorphisms are the Calabi homomorphism on stably displaceable sets.
MONDAY, December 6, 2010, 4:00 pm
Noboru Ito, "A colored Khovanov bicomplex"
December 10, 2010, 9:30 am
Andrew CottonClay, "Holomorphic Pairs of Pants in Mapping Tori"
Abstract: We consider invariants of mapping tori of symplectomorphisms of a symplectic surface S, such as the symplectic field theory, contact homology, or periodic Floer homology for the standard stable Hamiltonian structure on the mapping torus. These invariants involve counts of holomorphic curves in R times the mapping torus. We obtain a number theoretic description of all rigid holomorphic curves in the case S = T^2, and obtain various pairofpants invariants for symplectomorphisms on higher genus surfaces. Our method involves reinterpreting counts of holomorphic pairs of pants in R times the mapping torus as counts of index 1 triangles between Lagrangians in S x S for certain 1parameter families of almostcomplex structures.
December 10, 2010, 10:45 am
Timothy Nguyen, "The SeibergWitten Equations on Manifolds with Boundary"
Abstract: The analysis of the SeibergWitten equations have led to many important results in lowdimensional topology. These include the invariants defined by Witten for 4manifolds and the monopole Floer invariants for 3manifolds defined by KronheimerMrowka and others. In both these situations, the equations and their moduli space of solutions are studied on closed manifolds. In this talk, we study the analysis of the SeibergWitten equations on manifolds with boundary. First, we discuss the space of solutions to the SeibergWitten equations on 3manifolds with boundary. This solution space is infinite dimensional (even modulo gauge) since no boundary conditions are imposed on the equations. Second, we discuss how this solution space yields natural boundary conditions for the SeibergWitten equations on a cylindrical 4manifold R x Y, where Y is a 3manifold with boundary. We explain how the resulting nonlinear boundary value problem has wellposedness and compactness properties, and how these results therefore serve as foundational analysis for an eventual construction of a monopole Floer theory on manifolds with boundary.
December 17, 2010
Ben Mares, "Some analytic aspects of VafaWitten twisted N=4 supersymmetric YangMills theory"
Abstract: Given an oriented Riemannian fourmanifold equipped with a principal bundle, we investigate the moduli space of solutions to the VafaWitten equations. We establish various properties, computations, and estimates for these equations, and give a partial Uhlenbeck compactification of the moduli space.
Other relevant information
Other area seminars
 Columbia Geometric Topology Seminar
 Columbia Algebraic Geometry Seminar
 Princeton Topology 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.