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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.

Wednesday, March 4, 2015 - 14:00 ,
Location: Skiles 006 ,
Sudipta Kolay ,
Georgia Tech ,
Organizer: Sudipta Kolay

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.

Wednesday, February 11, 2015 - 14:00 ,
Location: Skiles 006 ,
Alan Diaz ,
Georgia Tech ,
Organizer:

Wednesday, February 4, 2015 - 14:00 ,
Location: Skiles 006 ,
James Conway ,
Georgia Tech ,
Organizer: James Conway

TBA

Wednesday, January 7, 2015 - 14:05 ,
Location: Skiles 006 ,
Peter Woolfitt ,
Georgia Tech ,
Organizer: Dan Margalit

Wednesday, December 3, 2014 - 14:00 ,
Location: Skiles 006 ,
Robert Krone ,
Georgia Tech ,
Organizer: Robert Krone

I will present a result of Klarreich on the boundary at infinity of the
complex of curves of a compact orientable surface. The complex of curves
is a delta-hyperbolic space so it has a boundary which is the set of
equivalence classes of quasi-geodesic rays. Klarreich shows that the
resulting space is homeomorphic to the space of minimal foliations of the
surface.