The SGGTC seminar meets on Fridays in Math 407, at 10:45 am unless noted otherwise (in red).
Previous semesters: 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.
Our email list.
Date  Speaker 
Title 
Sept. 5 1:15 pm 
Organizational Meeting 
Organizational Meeting Joint with Geometric Topology Seminar 
Sept. 12  Christopher Scaduto (UCLA) 
Instantons and odd Khovanov homology 
Sept. 19  Lena Gal (TelAviv University) 
Symmetric Selfadjoint Hopf categories and a categorical Heisenberg double 
Sept. 26  Laura Starkston (UT Austin) 
Symplectic fillings and star surgery 
Oct. 3  Yajing Liu (UCLA) 
Lspace surgeries on links 
Oct. 10 9:30 
SiuCheong Lau (Harvard) 
Generalized SYZ mirror symmetry 
10:45  Matt Hogancamp (Indiana) 
The stable KhovanovRozansky homology of torus knots 
Oct. 17  Andrew Manion (Princeton) 
U_q(gl(11))representations and OzsvathSzabo's new bordered theory 
Oct. 24 11:00 
Dan CristofaroGardiner (Harvard)
IAS, Simonyi Hall 101. 
Symplectic embeddings from concave toric domains into convex ones (Joint ColumbiaPrincetonIAS Symplectic Topology Seminar) 
1:30  Michael Hutchings (UC Berkeley) IAS, Simonyi Hall 101. 
Beyond ECH capacities
(Joint ColumbiaPrincetonIAS Symplectic Topology Seminar) 
Oct. 31  Lucas Culler (Princeton)

3manifolds modulo surgery triangles 
Nov. 7  Khoa Nguyen (Stanford) 
On symplectic homology of complement of a normal crossing divisor 
Nov. 11 3:00 
Anna Beliakova (Universität Zürich) Math 507 
Trace of the categorified quantum groups 
Nov. 14 10:45 
Fabian Haiden 
Stability in Fukaya categories of surfaces 
2:30  Mark McLean (Stony Brook) 
The Lefschetz Hyperplane Theorem is Mostly Wrong (symplectically speaking) 
Nov. 21 9:15 
Erkao Bao (UCLA) 
Definition of cylindrical contact homology in dimension 3 
2:30  Tye Lidman (UT Austin) 
Contact topology and the Cabling conjecture 
Nov. 28  No seminar  Thanksgiving holiday 

Dec. 3 9:00 
Maciej Borodzik (University of Warsaw) Math 528 
Deformation of singular points of plane curves from smooth point of view 
Dec. 5 9:30 
Vinoth Nandakumar 
Exotic tstructures for twoblock Springer fibers 
10:45  Aliakbar Daemi 
Abelian Gauge Theory, Knots, and odd Khovanov Homology 
Dec. 12  [First day of final exams] 
Abstracts
September 12, 2014: Christopher Scaduto, "Instantons and odd Khovanov homology"
Abstract: Consider the double cover of the 3sphere branched over a link. We will discuss how the instanton homology of this 3manifold is related to the Khovanov homology of the link. When signs (integer coefficients) are taken into account, the relevant link homology is odd Khovanov homology, which is genuinely distinct from Khovanov homology. This material is motivated by work of Ozsváth and Szabó in the HeegaardFloer setting.
September 19, 2014: Lena Gal, "Symmetric Selfadjoint Hopf categories and a categorical Heisenberg double"
Abstract: We use the language of higher category theory to define what we call a
"symmetric selfadjoint Hopf" (SSH) structure on a semisimple abelian category. SSH categories are the categorical analog of positive selfadjoint Hopf algebras studied by A. Zelevinsky. It follows from his work that for every positive selfadjoint Hopf algebra the Heisenberg double is equipped with a natural action on the algebra. We obtain categorical analogs of the Heisenberg double and its action from the SSH structure on a category in a canonical way. We exhibit the SSH structure on the category of polynomial functors. The categorical Heisenberg double in this case provides a categorification of the infinite dimensional Heisenberg algebra related to the categorification proposed by M. Khovanov. The preprint is available on arXiv:1406.3973.
September 26, 2014: Laura Starkston, "Symplectic fillings and star surgery"
Abstract: Although the existence of a symplectic filling is wellunderstood for many contact 3manifolds, complete classifications of all symplectic fillings of a particular contact manifold are more rare. Relying on a recognition theorem of McDuff for closed symplectic manifolds, we can understand this classification for certain Seifert fibered spaces with their canonical contact structures. In fact, even without complete classification statements, the techniques used can suggest constructions of symplectic fillings with interesting topology. These fillings can be used in cutandpaste operations called star surgery to construct examples of exotic 4manifolds.
October 3, 2014: Yajing Liu, "Lspace surgeries on links"
Abstract: An Lspace link is a link on which all large surgeries are Lspaces. These links turn out to be rich in geometry and simple in algebra. I will present some properties and examples of Lspace links in contrast to Lspace knots, give bounds on the ranks of their Floer homology and on the coefficients in the multivariable Alexander polynomials, and show that how to use ManolescuOzsvath link surgery formula to give a free resolution of the Floer homology of surgeries on any Lspace links. As a result, we compute the whole package of Heegaard Floer homology of surgeries on 2component Lspace links only in terms of Alexander polynomial and the surgery framing. This work is inspired by the work of OzsvathSzabo, GorskyNemethi, and J.Hom.
October 10, 2014, 9:30 a.m.: SiuCheong Lau, "Generalized SYZ mirror symmetry"
Abstract: Mirror symmetry conjecture reveals deep relations between symplectic and complex geometries. The conjecture has been verified in many interesting cases by explicit computations. However the computations do not explain why we should expect mirror symmetry. In this talk I will introduce our constructive approach to mirror symmetry, which has the advantage that it always comes with a functor which transforms Lagrangian submanifolds to twisted holomorphic vector bundles (or known as matrix factorizations) over the mirror, and hence explains why symplectic geometry is mirror to complex geometry. This is a joint work with CheolHyun Cho and Hansol Hong.
October 10, 2014, 10:45 a.m.: Matt Hogancamp, "The stable KhovanovRozansky homology of torus knots"
Abstract: In a series of surprising conjectures, GorskyOblomkovRasmussenShende relate KhovanovRozansky homologies of the torus knot T(p,q) with the representation theory of the rational Cherednik algebra for SL_p. One such conjecture states that the triply graded KhovanovRozansky homology has a welldefined limit as $q\to \infty$, and that this homology is very simple: it is a (super) polynomial ring. In this talk we discuss and outline a proof of this limiting version of their conjecture. Along the way we discuss a categorified Young symmetrizer, which plays an essential role in our proof.
October 17, 2014: Andrew Manion, " U_q(gl(11))representations and OzsvathSzabo's new bordered theory"
Abstract: I'll start with a brief overview of some recent constructions, due to Ozsvath and Szabo, of a bordered theory for knot Floer homology based on the Kauffmanstates Heegaard diagram for a knot. Then I'll discuss the decategorification of this theory and how it relates to representations of U_q(gl(11)). Finally, I'll talk about a more precise connection between one type of local OzsvathSzabo bimodule and the bimodules over quiver algebras defined by Khovanov and Seidel.
October 24, 2014, 11:00am: Dan CristofaroGardiner, " Symplectic embeddings from concave toric domains into convex ones"
Abstract: Embedded contact homology gives a sequence of obstructions to fourdimensional symplectic embeddings, called ECH capacities. These obstructions are known to be sharp in several interesting cases, for example for symplectic embeddings of one ellipsoid into another. We explain why ECH capacities give a sharp obstruction to embedding any "concave toric domain" into a "convex" one. We also explain why the ECH capacities of any concave or convex toric domain are determined by the ECH capacities of a corresponding collection of balls. Some of this is joint work with Keon Choi, David Frenkel, Michael Hutchings, and Vinicius Ramos.
October 24, 2014, 1:30pm: Michael Hutchings, " Beyond ECH capacities "
Abstract: ECH (embedded contact homology) capacities give obstructions to symplectically embedding one fourdimensional symplectic manifold with boundary into another. These obstructions are known to be sharp when the domain is a "concave toric domain" and the target is a "convex toric domainâ€ť (see previous talk). However ECH capacities often do not give sharp obstructions, for example in many cases when the domain is a polydisk. In this talk we explain how more refined information from ECH gives stronger symplectic embedding obstructions when the domain is a polydisk, or more generally a convex toric domain. We use these new obstructions to reprove a result of HindLisi on symplectic embeddings of a polydisk into a ball, and generalize this to obstruct some symplectic embeddings of a polydisk into an ellipsoid. We also obtain a new obstruction to symplectically embedding one polydisk into another, in particular proving the fourdimensional case of a conjecture of Schlenk.
October 31, 2014: Lucas Culler, "3manifolds modulo surgery triangles"
Abstract: Consider the abelian group $K_g$ generated by bordered 3manifolds with boundary a genus g surface $\Sigma_g$, modulo the relation that any three manifolds which are related by a surgery triangle sum to zero. In this talk I'll prove that $K_g$ is free and describe an explicit finite basis. This basis is of interest because it generates the category assigned to $\Sigma_g$ by any bordered Floer theory with exact triangles.
November 7, 2014: Khoa Nguyen, "On symplectic homology of complement of a normal crossing divisor"
Abstract: In this talk, we discuss our work in progress about how degeneration of the divisor at infinity into a normal crossing divisor affects the symplectic homology of an affine variety. From an antisurgery picture, by developing an antisurgery formula for symplectic homology similar to work by BourgeoisEkholmEliashberg, we show that essentially, the change in symplectic homology is reflected by the Hochschild invariants of the Fukaya category of a collection of Lagrangian spheres on the smooth divisor.
November 11, 2014, 3:00 p. m. : Anna Beliakova, "Trace of the categorified quantum groups"
Abstract: We show that the center and the trace of any 2representation of the KhovanovLauda 2category for any symmetrizable Lie algebra g admit an action of the current algebra U(g[t]). In particular, the 0th Hochschild (co)homology of the cyclotomic quotient is the (dual) Weyl module.
November 14, 2014, 10:45 a.m.: Fabian Haiden, "Stability in Fukaya categories of surfaces"
Abstract: I will report on recent joint work with L. Katzarkov and M. Kontsevich (arXiv:1409.8611) in which we construct Bridgeland stability conditions on partially wrapped Fukaya categories of surfaces. Stable objects in these stability conditions correspond to finitelength geodesics (with local system) with respect to some flat metric with conical singularities given by a quadratic differential. The proof relies on the fact that all objects in the derived Fukaya category of a surface are geometric, i.e. come from immersed curves with local system. Examples and some further directions will also be discussed.
November 14, 2014, 2:30 p.m.: Mark McLean, "The Lefschetz Hyperplane Theorem is Mostly Wrong (symplectically speaking)"
Abstract: We show that for any symplectic manifold of dimension 2n>4, there exists a symplectic hypersurface Poincare dual to some positive multiple of the symplectic form whose (n2)th Betti number is as large as we like. The idea here is to find an appropriate Liouville domain inside each of these symplectic manifolds and use Donaldson's asymptotically holomorphic techniques from his 1996 paper to find a symplectic hypersurface not intersecting some deformation of this Liouville domain.
November 21, 2014, 9:15 a.m.: Erkao Bao, " Definition of cylindrical contact homology in dimension 3"
Abstract: In this talk, we will give a rigorous definition of cylindrical contact homology for contact manifold of dimension 3, when there is no contractible Reeb orbit, and prove that it is an invariant of the contact structure. The proof is essentially based on some type of obstruction bundle calculations. Also, if time permits, we will talk about the case when there are contractible Reeb orbits. This talk is based on a joint work of Ko Honda and myself.
November 21, 2014, 2:30 p.m.: Tye Lidman, "Contact topology and the Cabling conjecture"
Abstract: The Cabling conjecture is a classical problem in threemanifold topology which attempts to characterize the knots in the threesphere for which Dehn surgery results in a nonprime manifold. We use standard results in three and fourdimensional contact and symplectic topology to study this problem. This is joint work with Steven Sivek.
December 3, 2014, 9:00 a.m.: Maciej Borodzik, "Deformation of singular points of plane curves from smooth point of view"
Abstract: Using Heegaard Floer theory we reprove a recent result by Gorsky and Nemethi about semicontinuity of semigroups under deformations of singular points. Unlike the original result, we add an extra assumption namely that the deformation is deltaconstant, however the proof is purely topological. We explain the geometric meaning of this extra assumption and show a generalization. The generalization suggests a possible difference between smooth concordance and analytic deformations. This is a joint work with Charles Livingston.
December 5, 2014, 9:30 a.m.: Vinoth Nandakumar, "Exotic tstructures for twoblock Springer fibers"
Abstract: We study the exotic tstructure on D_n, the derived category of coherent sheaves on the Springer fiber for a twoblock nilpotent (i.e. for a nilpotent matrix of type (m+n,n) in type A). Exotic tstructures were introduced by Bezrukavnikov and Mirkovic in order to study representations of Lie algebras in positive characteristic. Using work of Cautis and Kamnitzer, we construct functors between these categories D_n, indexed by affine tangles. We use these functors to enumerate the irreducibles in the heart of D_n by crossingless matchings, and compute the Ext's between these irreducibles. This is joint with R. Anno
December 5, 2014, 10:45 a.m.: Aliakbar Daemi, "Abelian Gauge Theory, Knots, and odd Khovanov Homology"
Abstract: In the first part of the talk I'll explain how one can use abelian gauge theory and Floer homological techniques to define a (3+1)dimensional "Topological Quantum Filed Theory". In the second talk some relations between this invariant and odd Khovanov homology will be discussed. No prior knowledge of gauge theory, Floer homology, or odd Khovanov homology will be expected.
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.