Seminars and Colloquia by Series

Overview of Yamabe problem

Series
Geometry Topology Student Seminar
Time
Wednesday, February 12, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey KalotiGeorgia Tech.
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.

Knot Contact Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, February 5, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jamie ConwayGeorgiaTech
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.

Non-lifting of a subgroup of the mapping class group

Series
Geometry Topology Student Seminar
Time
Wednesday, December 4, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert KroneGeorgia Tech
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.

Hirzebruch's signature theorem in dimension 4

Series
Geometry Topology Student Seminar
Time
Wednesday, November 20, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alan DiazSchool of Math, Georgia Tech
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.

Chern-Weil theory for vector bundles

Series
Geometry Topology Student Seminar
Time
Friday, November 15, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey KalotiGeorgia Tech.
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.

Homological Stability of Groups

Series
Geometry Topology Student Seminar
Time
Wednesday, October 30, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Becca WinarskiGeorgia Tech
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.

Riemann's mapping theorem for variable metrics

Series
Geometry Topology Student Seminar
Time
Wednesday, October 23, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jing HuGeorgia Tech
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.

Topological K-Theory

Series
Geometry Topology Student Seminar
Time
Wednesday, October 16, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shane ScottGeorgia Tech
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.

Exotic 7-Spheres

Series
Geometry Topology Student Seminar
Time
Wednesday, October 9, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jamie ConwayGeorgia Tech
We will discuss Milnor's classic proof of the existence of exotic smooth structures on the 7-sphere.

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