Wednesday, April 8, 2015 - 14:05 , Location: Skiles 006 , Xander Flood , Georgia Tech , email@example.com , Organizer: Alexander Flood
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.
Wednesday, April 1, 2015 - 14:05 , Location: Skiles 006 , Benjamin Ide , Georgia Tech , Organizer: Benjamin Ide
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.
Wednesday, March 25, 2015 - 14:05 , Location: Skiles 006 , Jonathan Paprocki , Georgia Tech , Organizer: Jonathan Paprocki
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).
Friday, March 13, 2015 - 13:00 , Location: Skiles 006 , John Etnyre , Georgia Tech , Organizer: John Etnyre
In this talk I will finish the proof that braid groups are linear using the Lawrence-Krammer representation.
Wednesday, March 11, 2015 - 14:00 , Location: Skiles 006 , John Etnyre , Georgia Tech , Organizer: John Etnyre
In this talk I will discuss the Lawrence-Krammer representation of the Braid Group and begin to sketch the the proof that braid groups are linear.
Friday, February 20, 2015 - 14:05 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Sudipta Kolay
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.
Wednesday, February 18, 2015 - 14:00 , Location: Skiles 006 , Jamie Conway , Georgia Tech , Organizer: James Conway
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.