Bethe Ansatz and problems of real and complex algebraic geometry Prof. Evgeny Mukhin Indiana-Purdue university, U.S.A. 23-12-05 Abstract 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.
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