Abstracts
for the Seminar

Fall 2015

**Speaker: **Nat Thiem, University of Colorado

**Title: **A representation theoretic approach to transportation polytopes

**Time:** 2:30 PM, Monday, October 26, 2015

**Place:** Malott 206

**Abstract:** Supercharacter theories have given us some combinatorial control over the wild representation theory of finite unipotent groups. One of the most striking examples is in the case of the maximal unipotent subgroups of the finite general linear groups, whose supercharacter theory is built on the combinatorics of set partitions; in fact, taken as a family, these representations give the Hopf algebra of symmetric functions in noncommuting variables. It turns out that set partitions naturally occur as integer lattice points contained in a family of transportation polytopes. This talk shows how to find the lattice points of arbitrary transportation polytopes in the representation theory of finite unipotent groups, and discusses some of the natural questions that this connection suggests.

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