### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

OCTOBER 26, 2018

**Speaker: **
Michael Dobbins, Binghamton University

**Title: ***
Grassmannians and Pseudosphere Arrangements
*

**Abstract: **
I will present an extension of vector configurations to more general
objects that have nicer combinatorial and topological properties,
namely weighted pseudosphere arrangements, as in the topological
representation theorem of oriented matroids. These form a metric
space, and in rank 3, are homotopy equivalent to the corresponding
Grassmannians. Also, the subspaces representing a fixed oriented
matroid are contractible. This is a sharp contrast with vector
configurations where the space of realizations can have the homotopy
type of any primary semialgebraic set even in rank 3. Work on these
spaces was partly motivated by combinatorial tools for working with
vector bundles.

**Time:** Friday, October 26, 2018, 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