Wednesday, March 6, 2013 - 13:00 , Location: Skiles 006 , Alan Diaz , Georgia Tech , Organizer:
I'll discuss Plamenevskaya's invariant of transverse knots, how it can be used to determine tightness of contact structures on some 3-manifolds, and efforts to understand more about this invariant. This is an Oral Comprehensive Exam; the talk will last about 40 minutes.
Wednesday, February 20, 2013 - 11:05 , Location: Skiles 006 , Becca Winarski , Georgia Tech , Organizer:
A conjecture of Ivanov asserts that finite index subgroups of the mapping class group of higher genus surfaces have trivial rational homology. Putman and Wieland use what they call higher Prym representations, which are extensions of the representation induced by the action of the mapping class group on homology, to better understand the conjecture. In particular, they prove that if Ivanov's conjecture is true for some genus g surface, it is true for all higher genus surfaces. On the other hand, they also prove that if there is a counterexample to Ivanov's conjecture, it is of a specific form.
Wednesday, February 13, 2013 - 13:00 , Location: Skiles 005 , Jamie Conway , Georgia Tech , Organizer: James Conway
Given any surface, we can construct its curve complex by considering isotopy classes of curves on the surface. If the surface has boundary, we can construct its arc complex similarly, with isotopy clasess of arcs, with endpoints on the boundary. In 1999, Masur and Minsky proved that these complexes are hyperbolic, but the proof is long and involved. This talk will discuss a short proof of the hyperbolicity of the curve and arc complex recently given by Hensel, Przytycki, and Webb.
Wednesday, January 30, 2013 - 13:00 , Location: Skiles 006 , Meredith Casey , Georgia Tech , Organizer: James Conway
Wednesday, January 30, 2013 - 13:00 , Location: Skiles 006 , Meredith Casey , Georgia Tech , Organizer:
This is an expository talk on the arc complex and translation distance of open book decompositions. We will discuss curve complexes, arc complex, open books, and finally the application to contact manifolds.
Wednesday, January 23, 2013 - 13:05 , Location: Skiles 006. , Amey Kaloti , Georgia Tech , Organizer:
This is continuation of talk from last week. Periodic orbits of flows on $3$ manifolds show very rich structure. In this talk we will try to prove a theorem of Ghrist, which states that, there exists vector fields on $S^3$ whose set of periodic orbits contains every possible knot and link in $S^3$. The proof relies on template theory.
Wednesday, November 14, 2012 - 14:05 , Location: Skiles 006 , Becca Winarski , Georgia Tech , Organizer:
We look at a paper of McMullen "Braid Groups and Hodge Theory" exploring representations of braid groups and their connections to arithemetic lattices.
Wednesday, October 31, 2012 - 14:00 , Location: Skiles 006. , Amey Kaloti , Georgia Tech , Organizer:
The goal of this talk is to study geography and classification problem for Stein fillings of contact structures supported by planar open books. In the first part we will prove that for contact structures supported by planar open books Stein fillings have a finite geography. In the second part we will outline an approach to classify Stein fillings of manifolds supported by planar open books.