### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

MARCH 25, 2016

**Speaker: **
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.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491