Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 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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