The Geometry and Topology Research Seminar regularly meets on Monday at 2:00 in Skiles 006 unless otherwise indicated.
Fall 2018
Date  Title  Speaker  Institute 
Dec. 3  Maximal Weinstein domains  Oleg Lazarev  Columbia University 
Nov 19  The arithmetic of orientationreversing mapping classes  Livio Liechti  ParisJussieu 
Nov 16  Counting incompressible surfaces and the 3Dindex  Stavros Garoufalidis  Georgia Tech & MPI 
Nov 12  Affine Grassmannians in motivic homotopy theory  Tom Bachmann  MIT 
Nov 5  A family of freely slice good boundary links  Min Hoon Kim  Korea Institute for Advanced Study 
Oct 29  Stable homotopy invariants for links Special place and time: UGA, Boyd 328, 4:00 pm 
Patrick Orson  Boston College 
Oct 29  A ribbon obstruction and derivatives of knots Special place and time: UGA, Boyd 328, 2:30 pm 
JungHwan Park  Georgia Tech 
Oct 22  Genuine Equivariant Operads  Luis Alexandre Pereira  Georgia Tech 
Oct 15  The transverse invariant and braid dynamics  Lev TovstopyatNelip  Boston College 
Oct 8  No Seminar: Fall Break  
Oct 1  The ribbon genus of a knotted surface Special Time: 3:30 
Jason Joseph  UGA 
Oct 1  A contact Fukaya category  Lenny Ng  Duke University 
Sept 24  Link Concordance and Groups  Miriam Kuzbary  Rice University 
Sept 17  Nonisotopic embeddings of contact manifolds  John Etnyre  Georgia Tech 
Sept 10  Rational cobordisms and integral homology  JungHwan Park  Georgia Tech 
Sept 3  No Seminar: Labor Day  
Aug 27  Khovanov homology via immersed curves in the 4punctured sphere Special place and time: UGA, Boyd 328, 4:00 pm 
Artem Kotelskiy  Indiana University 
Aug 27 
Homological knot invariants and the unknotting numberUnknotting number is one of the simplest, yet mysterious, knot invariants. For example, it is not known whether it is additive under connected sum or not. In this talk, we will construct lower bounds for the unknotting number using two homological knot invariants: knot Floer homology, and (variants of) Khovanov homology. Unlike most lower bounds for the unknotting number, these invariants are not lower bound for the slice genus and they only vanish for the unknot. Parallely, we will discuss connections between knot Floer homology and (variants of) Khovanov homology. One main conjecture relating knot Floer homology and Khovanov homology is that there is a spectral sequence from Khovanov homology to knot Floer homology. If time permits, we will sketch an algebraically defined knot invariant, for which there is a spectral sequence from Khovanov homology converging to it. The construction is inspired by counting holomorphic discs, so we expect it to recover the knot Floer homology. This talk is based on joint works with Eaman Eftekhary and Nathan Dowlin.
Special place and time: UGA, Boyd 328, 2:30 pm 
Akram Alishahi  Columbia University 
Date  Title  Speaker  Institute 
December 3  Maximal Weinstein domains  Oleg Lazarev  Columbia University 
November 19  The arithmetic of orientationreversing mapping classes  Livio Liechti  ParisJussieu 
November 19 
Counting incompressible surfaces and the 3DindexI will explain some connections between the counting of incompressible surfaces in hyperbolic 3manifolds with boundary and the 3Dindex of DimofteGaiottoGukov. Joint work with N. Dunfield, C. Hodgson and H. Rubinstein, and, as usual, with lots of examples and patterns.

Stavros Garoufalidis  Georgia Tech & MPI 
November 12  Affine Grassmannians in motivic homotopy theory  Tom Bachmann  MIT 
November 5 
A family of freely slice good boundary linksThe still open topological 4dimensional surgery conjecture is equivalent to the statement that all good boundary links are freely slice. In this talk, I will show that every good boundary link with a pair of derivative links on a Seifert surface satisfying a homotopically trivial plus assumption is freely slice. This subsumes all previously known methods for freely slicing good boundary links with two or more components, and provides new freely slice links. This is joint work with Jae Choon Cha and Mark Powell.

Min Hoon Kim  Korea Institute for Advanced Study 
October 29  Stable homotopy invariants for links Special place and time: UGA, Boyd 328, 4:00 pm 
Patrick Orson  Boston College 
October 29  A ribbon obstruction and derivatives of knots Special place and time: UGA, Boyd 328, 2:30 pm 
JungHwan Park  Georgia Tech 
October 22  TBA by Luis Alexandre Pereira  Luis Alexandre Pereira  Georgia Tech 
October 15 
The transverse invariant and braid dynamics
Let K be a link braided about an open book (B,p) supporting a contact manifold (Y,x). K and B are naturally transverse links. We prove that the hat version of the transverse link invariant defined by Baldwin, VelaVick and Vertesi is nonzero for the union of K with B. As an application, we prove that the transverse invariant of any braid having fractional Dehn twist coefficient greater than one is nonzero. This generalizes a theorem of Plamenevskaya for classical braid closures. 
Lev TovstopyatNelip  Boston College 
October 8  No Seminar: Fall Break  
October 1  The ribbon genus of a knotted surface Special Time: 3:30 
Jason Joseph  UGA 
October 1 
A contact Fukaya categoryI’ll describe a way to construct an Ainfinity category associated to a contact manifold, analogous to a Fukaya category for a symplectic manifold. The objects of this category are Legendrian submanifolds equipped with augmentations. Currently we’re focusing on standard contact R^3 but we’re hopeful that we can extend this to other contact manifolds. I’ll discuss some properties of this contact Fukaya category, including generation by unknots and a potential application to proving that
augmentations = sheaves”. This is joint work in progress with Tobias Ekholm and Vivek Shende. 
Lenny Ng  Duke University 
September 24 
Link Concordance and GroupsSince its introduction in 1966 by Fox and Milnor the knot concordance group has been an invaluable algebraic tool for examining the relationships between 3 and 4 dimensional spaces. Though knots generalize naturally to links, this group does not generalize in a natural way to a link concordance group. In this talk, I will present joint work with Matthew Hedden where we define a link concordance group based on the “knotification” construction of Peter Ozsvath and Zoltan Szabo. This group is compatible with Heegaard Floer theory and, in fact, much of the work on Heegaard Floer theory for links has implied a study of these objects. Moreover, we have constructed a generalization of Milnor’s grouptheoretic higher order linking numbers in a novel context with implications for our link concordance group.

Miriam Kuzbary  Rice University 
September 17 
Nonisotopic embeddings of contact manifoldsThe study of transverse knots in dimension 3 has been instrumental in the development of 3 dimensional contact ge ometry. One natural generalization of transverse knots to higher dimensions is contact submanifolds. Embeddings of one contact manifold into another satisfies an hprinciple for codimension greater than 2, so we will discuss the case of codimension 2 contact embeddings. We will give the first pair of nonisotopic contact embeddings in all dimensions (that are formally isotopic).

John Etnyre  Georgia Tech 
September 10 
Rational cobordisms and integral homologyWe show that for any connected sum of lens spaces L there exists a connected sum of lens spaces X such that X is rational homology cobordant to L and if Y is rational homology cobordant to X, then there is an injection from H_1(X; Z) to H_1(Y; Z). Moreover, as a connected sum of lens spaces, X is uniquely determined up to orientation preserving diffeomorphism. As an application, we show that the natural map from the Z/pZ homology cobordism group to the rational homology cobordism group has large cokernel, for each prime p. This is joint work with Paolo Aceto and Daniele Celoria.

JungHwan Park  Georgia Tech 
September 3  No Seminar: Labor Day  
August 27 
Khovanov homology via immersed curves in the 4punctured sphereWe will describe a geometric interpretation of Khovanov homology as Lagrangian Floer homology of two immersed curves in the 4punctured 2dimensional sphere. The main ingredient is a construction which associates an immersed curve to a 4ended tangle. This curve is a geometric way to represent Khovanov (or BarNatan) invariant for a tangle. We will show that for a rational tangle the curve coincides with the representation variety of the tangle complement. The construction is inspired by a result of [Hedden, Herald, Hogancamp, Kirk], which embeds 4ended reduced Khovanov arc algebra (or, equivalently, BarNatan dotted cobordism algebra) into the Fukaya category of the 4punctured sphere. The main tool we will use is a category of peculiar modules, introduced by Zibrowius, which is a model for the Fukaya category of a 2sphere with 4 discs removed. This is joint work with Claudius Zibrowius and Liam Watson.

Artem Kotelskiy  Indiana University 
Special time and place:  UGA, Boyd 328  4:00 pm  
August 27 
Homological knot invariants and the unknotting numberUnknotting number is one of the simplest, yet mysterious, knot invariants. For example, it is not known whether it is additive under connected sum or not. In this talk, we will construct lower bounds for the unknotting number using two homological knot invariants: knot Floer homology, and (variants of) Khovanov homology. Unlike most lower bounds for the unknotting number, these invariants are not lower bound for the slice genus and they only vanish for the unknot. Parallely, we will discuss connections between knot Floer homology and (variants of) Khovanov homology. One main conjecture relating knot Floer homology and Khovanov homology is that there is a spectral sequence from Khovanov homology to knot Floer homology. If time permits, we will sketch an algebraically defined knot invariant, for which there is a spectral sequence from Khovanov homology converging to it. The construction is inspired by counting holomorphic discs, so we expect it to recover the knot Floer homology. This talk is based on joint works with Eaman Eftekhary and Nathan Dowlin.

Akram Alishahi  Columbia University 
Special time and place:  UGA, Boyd 328  2:30 pm 
Spring 2018
coming soon