Speaker: Brent Doran, ETH
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.
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
Tel. 703-993-1460, Fax. 703-993-1491