Seminars and Colloquia by Series

Non-looseness of non-loose knots

Series
Geometry Topology Seminar
Time
Monday, March 3, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ken Baker – University of Miami
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.

Hamiltonian Circle Actions with Isolated Fixed Points on 6-Dimensional Symplectic Manifolds

Series
Geometry Topology Seminar
Time
Monday, February 17, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Andrew Fanoe – Morehouse College
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.

Convex cocompactness in mapping class groups via quasiconvexity in right-angled Artin groups

Series
Geometry Topology Seminar
Time
Monday, February 10, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Johanna Mangahas – U at Buffalo
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.

Smooth 4-manifolds, surface diagrams and holomorphic polygons

Series
Geometry Topology Seminar
Time
Monday, February 3, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan Williams – University of Georgia
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.

Comparing the slice and ribbon genera of knots via braided surfaces

Series
Geometry Topology Seminar
Time
Monday, January 27, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mark Hughes – SUNY, Stony Brook
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.

A categorification of the cut and flow lattices of graphs

Series
Geometry Topology Seminar
Time
Monday, January 13, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zsuzsanna Dancso – University of Toronto –
We discuss a simple construction a finite dimensional algebra("bipartite algebra") to a bipartite oriented graph, and explain how thestudy of the representation theory of these algebras produces acategorification of the cut and flow lattices of graphs. I'll also mentionwhy we suspect that bipartite algebras should arise naturally in severalother contexts. This is joint work with Anthony Licata.

Some metric properties of Houghton's groups

Series
Geometry Topology Seminar
Time
Monday, January 6, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sean Cleary – CUNY
Houghton's groups are a family of subgroups of infinite permutation groups known for their cohomological properties. Here, I describe some aspects of their geometry and metric properties including families of self-quasi-isomtries. This is joint work with Jose Burillo, Armando Martino and Claas Roever.

Galois-equivariant and motivic homotopy

Series
Geometry Topology Seminar
Time
Monday, December 9, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kyle Ormsby – MIT
For a group G, stable G-equivariant homotopy theory studies (the stabilizations of) topological spaces with a G-action up to G-homotopy. For a field k, stable motivic homotopy theory studies varieties over k up to (a stable notion of) homotopy where the affine line plays the role of the unit interval. When L/k is a finite Galois extension with Galois group G, there is a functor F from the G-equivariant stable homotopy category to the stable motivic homotopy category of k. If k is the complex numbers (or any algebraically closed characteristic 0 field) and L=k (so G is trivial), then Marc Levine has shown that F is full and faithful. If k is the real numbers (or any real closed field) and L=k[i], we show that F is again full and faithful, i.e., that there is a "copy" of stable C_2-equivariant homotopy theory inside of the stable motivic homotopy category of R. We will explore computational implications of this theorem.This is a report on joint work with Jeremiah Heller.

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