Laura Anderson, Binghamton University
Title: Phased matroids and matroids over hyperfields
Abstract: A matroid is a combinatorial analog to a subspace of a vector space $F^n$, where $F$ is an arbitrary field, and an oriented matroid is a matroid with extra structure analogous to the case $F=\mathbb R$. This extra structure leads to surprisingly rich interaction between combinatorics, geometry, and topology, and so it is natural to look for a generalization of this corresponding to $F=\mathbb C$, or for other fields. In a 2012 paper Emanuele Delucchi and I laid the foundations for such a theory for $F=\mathbb C$, and in very recent work Matt Baker has put nearly all these types of theories into a beautiful common framework. This talk will trace the development of this line of thought and discuss some of the many new questions opened by Baker's work.Time: Friday, March 25, 2016, 3:30-4:20 p.m.
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
Tel. 703-993-1460, Fax. 703-993-1491