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Martin Lorenz, Temple University
This is the first in a series of three lectures that will be accessible to students, including everybody currently taking Math 8011. I will start by briefly reviewing some material that was covered in Math 8011 this semester: the definition of the braid groups (by generators and relations), the visualization of braids (by braid diagrams), and some standard homomorphisms. Then I will dig a little deeper into the structure of the braid groups using the book by Kassel and Turaev as a reference.
Sara Leshen, Vanderbilt University
The Uncertainty Principle implies that a function and its Fourier transform cannot both be well-localized. The Balian-Low theorem is a form of the Uncertainty Principle for Riesz bases. In this joint work with A. Powell, we prove a new version of the Balian-Low theorem for Gabor Schauder bases generated by compactly supported functions. Moreover, we show that the classical Balian-Low theorem for Riesz bases does not hold for Schauder bases.
Sunder Sethuraman, University of Arizona
A GEM (Griffiths-Engen-McCloskey) sequence specifies the (random) proportions in splitting a `resource' infinitely many ways. Such sequences form the backbone of `stick breaking' representations of Dirichlet processes used in nonparametric Bayesian statistics. In this talk, we consider the connections between a class of generalized `stick breaking' processes, an intermediate structure via `clumped' GEM sequences, and the occupation laws of certain time-inhomogeneous Markov chains.
Vasily Dolgushev, Temple University
I will introduce a functor from a poset of certain finite index normal subgroups of the braid group on 4 strands to the category finite groupoids. The limit of this functor coincides with the profinite version of the Grothendieck-Teichmueller group introduced by Vladimir Drinfeld in 1990. My interest in this functor is motivated by the famous question posed by Yasutaka Ihara at the ICM of 1990. This talk is based on a joint work with Khanh Le and Aidan Lorenz.
Ben Stucky, University of Oklahoma
There are no conferences next week.