Bethe Ansatz and problems of real and complex algebraic geometry
Prof. Evgeny Mukhin
Indiana-Purdue university, U.S.A.
We will explain that the Bethe Ansatz method in integrable systems gives a way to study problems of Schubert Calculus. In particular we will outline a proof of the Shapiro conjecture and a reformulation of the transversality of intersections of Schubert cycles in terms of simlicity of spectrum of some linear operators. Time permitting, we will discuss a version of Schubert calculus related to Bethe Ansatz for root systems of type B and C.