## Seminar:

Fall 2011, Thursdays, Milner 216, 4:00-4:50 PM
__ Date:__ ** September 22 **

**" Mini-Talk "**

* Prof. David Kerr

* Prof. Frank Sottile

* Prof. David Kerr

* Prof. Frank Sottile

__Abstract__ *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.

Abstract:

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.