UIUC Dept. of Mathematics Seminar Calendar

    September 2009          October 2009          November 2009    
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Friday, October 2, 2009

Algebra, Geometry and Combinatorics Seminar
3:00 pm in 445 Altgeld Hall, Friday, October 2, 2009

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Submitted by llpku.

Eugene Mukhin (Indiana University-Purdue University Indianapolis)
Algebraic Bethe Ansatz
Abstract: The method of algebraic Bethe Ansatz can be used to connect the Representation Theory (over complex numbers) to many areas of mathematics, including Integrable Systems (the KDV and KP hierarchies, the Calogero-Moser system), Special Functions (orthogonal and multiple orthogonal polynomials, hypergeometric solutions of the KZ equations), Algebraic Geometry (Schubert Calculus, the B. and M. Shapiro conjecture), Combinatorics (Kostka polynomials, Capelli identities, crystalls). These relations produce a number of difficult and important theorems. I will survey some recent results in this area. (Based on a joint project with V. Tarasov and A. Varchenko.)