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.
Monday, January 27, 2014 - 14:00 , Location: Skiles 006 , Mark Hughes , SUNY, Stony Brook , Organizer: John Etnyre
In this talk I will discuss bounds on the slice genus of aknot coming from it's representation as a braid closure, starting withthe slice-Bennequin inequality. From there I will use surfacebraiding techniques of Rudolph and Kamada to exhibit a new lower boundon the ribbon genus of a knot, given some knowledge about what slicesurfaces it bounds.