Mathematics Graduate Students Organization

Seminar:

Date: September 22

D. Kerr: "Paradoxicality in dynamics and operator algebras"

Abstract: The Banach-Tarski paradox asserts that a ball in Euclidean 3-space can be cut up into finitely many pieces which can be transformed by rigid motions to construct two copies of the ball. I will describe how the phenomena surrounding this paradox have played a fundamental role in the development of operator algebra theory and its connections to dynamics, and discuss a number of problems of current research interest in this direction.

F. Sottile: "The control of linear systems and the Schubert calculus"

Abstract: Algebraic geometry enjoys many applications outside of mathematics. One old(er) application is in the theory of linear systems, where a fundamental object is naturally a rational curve in a Grassmannian, and a fundamental problem, that of pole-assignability, has a natural formulation in terms of the Schubert calculus. This link has been very productive for systems theory.

My talk will explain why the geometry of Grassmannians is relevant to systems theory, and it will mention some open problems in algebraic geometry that have recently arisen from this interaction.