Monday, April 14, 2014 - 14:00 , Location: Skiles 006 , David Krcatovich , MSU , Organizer: John Etnyre
The set of knots up to a four-dimensional equivalence relation can be given the structure of a group, called the (smooth) knot concordance group. We will discuss how to compute concordance invariants using Heegaard Floer homology. We will then introduce the idea of a "reduced" knot Floer complex, see how it can be used to simplify computations, and give examples of how it can be helpful in distinguishing knots which are not concordant.
Friday, April 11, 2014 - 13:05 , Location: Skiles 006 , Christian Zickert , University of Maryland , email@example.com , Organizer: Stavros Garoufalidis
The Ptolemy coordinates are efficient coordinates for computingboundary-unipotent representations of a 3-manifold group in SL(2,C). Wedefine a slightly modified version which allows you to computerepresentations that are not necessarily boundary-unipotent. This givesrise to a new algorithm for computing the A-polynomial.
Monday, April 7, 2014 - 14:05 , Location: Skiles 006 , Xingru Zhang , SUNY Buffalo , Organizer: Thang Le
We show that each (p,q)-torus knot in the 3-sphere is determined by its A-polynomial and its knot Floer homology. This is joint work with Yi Ni.
Monday, March 31, 2014 - 14:05 , Location: Skiles 006 , Kevin Wortman , University of Utah , Organizer: Dan Margalit
Suppose that F is a field with p elements, and let G be the finite-index congruence subgroup of SL(n, F[t]) obtained as the kernel of the homomorphism that reduces entries in SL(n, F[t]) modulo the ideal (t). Then H^(n-1)(G;F) is infinitely generated. I'll explain the ideas behind the proof of the above result, which is a special case of a result that applies to any noncocompact arithmetic group defined over function fields.
Monday, March 10, 2014 - 14:05 , Location: Skiles 006 , Anh Tran , Ohio State University (Columbus) , Organizer: Thang Le
A non-trivial group G is called left-orderable if there exists a strict total ordering < on its elements such that g
Monday, March 3, 2014 - 14:00 , Location: Skiles 006 , Ken Baker , University of Miami , Organizer: John Etnyre
A contact structure on a 3-manifold is called overtwisted ifthere is a certain kind of embedded disk called an overtwisted disk; it istight if no such disk exists. A Legendrian knot in an overtwisted contact3-manifold is loose if its complement is overtwisted and non-loose if itscomplement is tight. We define and compare two geometric invariants, depthand tension, that measure how far from loose is a non-loose knot. This isjoint work with Sinem Onaran.
Monday, February 17, 2014 - 14:00 , Location: Skiles 006 , Andrew Fanoe , Morehouse College , Organizer: John Etnyre
The question of what conditions guarantee that a symplectic$S^1$ action is Hamiltonian has been studied for many years. Sue Tolmanand Jonathon Weitsman proved that if the action is semifree and has anon-empty set of isolated fixed points then the action is Hamiltonian.Furthermore, Cho, Hwang, and Suh proved in the 6-dimensional case that ifwe have $b_2^+=1$ at a reduced space at a regular level $\lambda$ of thecircle valued moment map, then the action is Hamiltonian. In this paper, wewill use this to prove that certain 6-dimensional symplectic actions whichare not semifree and have a non-empty set of isolated fixed points areHamiltonian. In this case, the reduced spaces are 4-dimensional symplecticorbifolds, and we will resolve the orbifold singularities and useJ-holomorphic curve techniques on the resolutions.
Monday, February 10, 2014 - 14:05 , Location: Skiles 006 , Johanna Mangahas , U at Buffalo , Organizer: Dan Margalit
I'll talk about joint work with Sam Taylor. We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. We use this to construct convex cocompact subgroups of Mod(S) whose orbit maps into the curve complex have small Lipschitz constants.
Monday, February 3, 2014 - 14:00 , Location: Skiles 006 , Jonathan Williams , University of Georgia , Organizer: John Etnyre
The topic of smooth 4-manifolds is a long established, yetunderdeveloped one. Its mystery lies partly in its wealth of strangeexamples, coupled with a lack of generally applicable tools to putthose examples into a sensible framework, or to effectively study4-manifolds that do not satisfy rather strict criteria. I will outlinerecent work that associates objects from symplectic topology, calledweak Floer A-infinity algebras, to general smooth, closed oriented4-manifolds. As time permits, I will speculate on a "genus-g Fukayacategory of smooth 4-manifolds.