### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

FEBRUARY 20, 2017

**Speaker: **
Brent Doran, ETH

**Title: ***
Hidden symmetries in geometry, arithmetic, and physics
*

**Abstract:**
Most of the complexity of algebraic group actions (symmetries) lies in their additive subgroups. In fact, additive group actions are baked-in to the fundamental structure of algebraic geometry. Thus many problems with no evident internal symmetry actually do admit a natural presentation via such a "hidden" symmetry. This provides a uniform approach to a number of well-known questions across many disciplines: interpolation theory, geometry, arithmetic, and real world quantum physics. In practice, much of the art lies in finding the ``correct" combinatorics for the problem at hand (moment polytopes, Okounkov bodies, lattice geometry, etc.), and much of the computational complexity can be seen in terms of high school algebra.

**Time:** Monday, February 20, 2017, 12:00 - 1:00 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 11:30 a.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