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Wednesday, April 23, 2014 - 14:00 ,
Location: Skiles 006 ,
Ece Gülşah Çolak ,
Bülent Ecevit University and Georgia Tech ,
ecolak3@math.gatech.edu ,
Organizer:

We will discuss Etnyre and Honda's proof of the classification of Legendrian positive torus knots in the tight contact 3-sphere up to Legendrian isotopy by using the tools from convex surface theory.

Wednesday, March 12, 2014 - 13:59 ,
Location: Skiles 006 ,
Dheeraj Kulkarni ,
Georgia Tech. ,
kulkarni@math.gatech.edu ,
Organizer:

In this talk, we will discuss a result due to Gabai which states that a minimal genus Seifert surface for a knot in 3-sphere can be realized as a leaf of a taut foliation of the knot complement. We will give a fairly detailed outline of the proof. In the process, we will learn how to construct taut foliations on knot complements.

Wednesday, February 12, 2014 - 14:05 ,
Location: Skiles 006. ,
Amey Kaloti ,
Georgia Tech. ,
Organizer:

We will give an overview of ideas that go into solution of Yamabe problem: Given a
compact Riemannian manifold (M,g) of dimension n > 2, find a metric conformal to g with
constant scalar curvature.

Wednesday, February 5, 2014 - 14:00 ,
Location: Skiles 006 ,
Jamie Conway ,
GeorgiaTech ,
Organizer: James Conway

Knot Contact Homology is a powerful invariant assigning to each smooth knot in three-space a differential graded algebra. The homology of this algebra is in general difficult to calculate. We will discuss the cord algebra of a knot, which allows us to calculate the grading 0 knot contact homology. We will also see a method of extracting information from augmentations of the algebra.

Wednesday, December 4, 2013 - 14:00 ,
Location: Skiles 006 ,
Robert Krone ,
Georgia Tech ,
Organizer: Robert Krone

The mapping class group of a surface is a quotient of the group of orientation preserving diffeomorphisms. However the mapping class group generally can't be lifted to the group of diffeomorphisms, and even many subgroups can't be lifted. Given a surface S of genus at least 2 and a marked point z, the fundamental group of S naturally injects to a subgroup of MCG(S,z). I will present a result of Bestvina-Church-Souto that this subgroup can't be lifted to the diffeomorphisms fixing z.

Wednesday, November 20, 2013 - 14:00 ,
Location: Skiles 006 ,
Alan Diaz ,
School of Math, Georgia Tech ,
adiaz@math.gatech.edu ,
Organizer: Alan Diaz

We'll prove the simplest case of Hirzebruch's signature
theorem, which relates the first Pontryagin number of a smooth 4-manifold
to the signature of its intersection form. If time permits, we'll discuss
the more general case of 4k-manifolds. The result is relevant to Prof.
Margalit's ongoing course on characteristic classes of surface bundles.

Friday, November 15, 2013 - 14:05 ,
Location: Skiles 006. ,
Amey Kaloti ,
Georgia Tech. ,
Organizer:

Given a vector bundle over a smooth manifold, one can give an alternate
definition of characteristic classes in terms of geometric data, namely connection
and curvature. We will see how to define Chern classes and Euler class for the a
vector bundle using this theory developed in mid 20th century.

Wednesday, November 13, 2013 - 14:05 ,
Location: Skiles Basement ,
Charles Watts ,
Student ,
Organizer:

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.