Seminars and Colloquia by Series

Higher Prym Representations of the Mapping Class Group

Series
Geometry Topology Student Seminar
Time
Wednesday, February 20, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Becca Winarski – Georgia Tech
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.

Hyperbolicity of the Arc and Curve Complex

Series
Geometry Topology Student Seminar
Time
Wednesday, February 13, 2013 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jamie Conway – Georgia Tech
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.

The Arc Complex and Open Book Decompositions

Series
Geometry Topology Student Seminar
Time
Wednesday, January 30, 2013 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Meredith Casey – Georgia Tech
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.

Knots and Dynamics II

Series
Geometry Topology Student Seminar
Time
Wednesday, January 23, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey Kaloti – Georgia Tech
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.

Braid Groups and Hodge Theory

Series
Geometry Topology Student Seminar
Time
Wednesday, November 14, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Becca Winarski – Georgia Tech
We look at a paper of McMullen "Braid Groups and Hodge Theory" exploring representations of braid groups and their connections to arithemetic lattices.

Stein fillings of planar open books.

Series
Geometry Topology Student Seminar
Time
Wednesday, October 31, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey Kaloti – Georgia Tech
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.

Toric Manifolds - Four Dimensions from Two

Series
Geometry Topology Student Seminar
Time
Wednesday, September 12, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jamie Conway – Georgia Tech
We will investigate a method of "seeing" properties of four dimensional symplectic spaces by looking at two dimensional pictures. We will see how to calculate the Euler characteristic, identify embedded surfaces, see intersection numbers, and how to see induced contact structures on the boundary of these manifolds.

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