Abstracts
for the Seminar

Spring 2020

**Speaker: **
Ed Swartz, Cornell University

**Title: **Polymatroids are to finite groups as matroids are to finite fields

**Time:** 2:30 PM, Monday, Feb. 10, 2020

**Place:** Malott 206

**Abstract:** In 1935 Whitney introduced matroids as a combinatorial abstraction of linear independence. Since then there has been a strong connection between matroids, and the geometry and combinatorics of finite dimensional vector spaces over finite fields.

Polymatroids are a very simple to define generalization of matroids. We will try to convince the audience that the title is nowhere near as crazy as it sounds. We will take classic examples of how matroids and vector spaces over finite fields interact, and show that they are special cases of how polymatroids and finite groups interact.

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