Date:	Mon, April 29, 2013
Time:	17:15
Place:	Research II Lecture Hall

Abstract: Rings of differential operators originated in quantum mechanics, and shortly thereafter found applications in analysis as a way to algebraize problems in PDE's. Modules for such rings are called D-modules (D for "differential"). In this talk, I'll introduce the Weyl algebra, an algebra of polynomial differential operators, and explain the relationship between its modules and solutions to differential equations. This relationship has important applications, notably the Frobenius theorem on linear systems of PDE's and the solution to Hilbert's 21st problem. Time permitting, I will explain (without proof) the statements of these theorems.