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Wednesday, October 30, 2013 - 14:05 ,
Location: Skiles 006 ,
Becca Winarski ,
Georgia Tech ,
Organizer:

Let MCG(g) be the mapping class group of a surface of genus g. For
sufficiently large g, the nth homology (and cohomology) group of MCG(g) is
independent of g. Hence we say that the family of mapping class groups
satisfies homological stability. Symmetric groups and braid groups also
satisfy homological stability, as does the family of moduli spaces of
certain higher dimensional manifolds. The proofs of homological stability
for most families of groups and spaces follow the same basic structure, and
we will sketch the structure of the proof in the case of the mapping class
group.

Wednesday, October 23, 2013 - 14:00 ,
Location: Skiles 006 ,
Jing Hu ,
Georgia Tech ,
Organizer:

Consider the Beltrami equation f_{\bar z}=\mu *f_{z}. The prime aim is to
investigate f in its dependence on \mu. If \mu depends analytically,
differentiably, or continuously on real parameters, the same is true for f;
in the case of the plane, the results holds also for complex parameters.

Wednesday, October 16, 2013 - 14:05 ,
Location: Skiles 006 ,
Shane Scott ,
Georgia Tech ,
scottsha@gatech.edu ,
Organizer: Shane Scott

To any compact Hausdorff space we can assign the ring of (classes of)
vector bundles under the operations of direct sum and tensor product. This assignment
allows the construction of an extraordinary cohomology theory for which the long
exact sequence of a pair is 6-periodic.

Wednesday, October 9, 2013 - 14:00 ,
Location: Skiles 006 ,
Jamie Conway ,
Georgia Tech ,
Organizer: James Conway

We will discuss Milnor's classic proof of the existence of exotic smooth structures on the 7-sphere.

Wednesday, September 25, 2013 - 14:05 ,
Location: Skiles 006. ,
Amey Kaloti ,
Georgia Tech ,
Organizer:

The aim of this talk is to give fairly self contained proof of the following result due to Eliashberg. There is exactly one holomorphically fillable contact structure on $T^3$. If time permits we will try to indicate different notions of fillability of contact manifolds in dimension 3.

Wednesday, March 13, 2013 - 13:00 ,
Location: Skiles 006 ,
Hyunshik Shin ,
Georgia Tech ,
Organizer:

We will briefly talk about the introduction to Thruston norm and fibered face theory. Then we will discuss polynomial invariants for fibered 3-manifolds, so called Teichmuller polynomials. I will give an example for a Teichmuller polynomial and by using it, determine the stretch factors (dilatations) of a family of pseudo-Anosov homeomorphisms.

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.