Seminars and Colloquia by Series

Complex-oriented cohomology theories and Quillen's theorem Part I

Series
Geometry Topology Student Seminar
Time
Wednesday, April 8, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Xander Flood – Georgia Tech –
Complex-oriented cohomology theories are a class of generalized cohomology theories with special properties with respect to orientations of complex vector bundles. Examples include all ordinary cohomology theories, complex K-theory, and (our main theory of interest) complex cobordism.In two talks on these cohomology theories, we'll construct and discuss some examples and study their properties. Our ultimate goal will be to state and understand Quillen's theorem, which at first glance describes a close relationship between complex cobordism and formal group laws. Upon closer inspection, we'll see that this is really a relationship between C-oriented cohomology theories and algebraic geometry.

Representability of Cohomology

Series
Geometry Topology Student Seminar
Time
Wednesday, April 1, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Benjamin Ide – Georgia Tech
In this talk, I prove that there is a bijection between [X, K(\pi, n)] and H^n(X; \pi). The proof is a good introduction to obstruction theory.

Quantum representations of braids

Series
Geometry Topology Student Seminar
Time
Wednesday, March 25, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan Paprocki – Georgia Tech
Solutions to the Yang-Baxter equation are one source of representations of the braid group. Solutions are difficult to find in general, but one systematic method to find some of them is via the theory of quantum groups. In this talk, we will introduce the Yang-Baxter equation, braided bialgebras, and the quantum group U_q(sl_2). Then we will see how to obtain the Burau and Lawrence-Krammer representations of the braid group as summands of natural representations of U_q(sl_2).

Vector Fields on Spheres

Series
Geometry Topology Student Seminar
Time
Friday, February 20, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta Kolay – Georgia Tech

Please Note: This is a project for Prof. Wickelgren's course on Stable Homotopy Theory.

In this talk, I will show using Clifford algebras that there are ρ(n)-1 linearly independent vector fields on the unit sphere in the n dimensional Euclidean space, where ρ(n) is the Radon-Hurwitz number.

Braid Theory: Burau and Gassner Representations

Series
Geometry Topology Student Seminar
Time
Wednesday, February 18, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jamie Conway – Georgia Tech
We will describe the Burau representation of the braid group and the related Gassner representation of the pure braid group. We will explore how the Burau representation is related to the Alexander polynomial.

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