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Recruitment Talk -- Integrability, Enumerative Counts, and Opers

The Golden Hourglass by Craig Schaffer
January 23, 2023
4:15 pm - 5:15 pm
CH 240

Speaker:  Peter Koroteev

Title:  Integrability, Enumerative Counts, and Opers

Abstract:  I will describe how classical and quantum integrability can be understood using the language of algebraic geometry and representation theory. First I will introduce classical many-body systems and quantum spin chains. The former can be described in purely algebraic terms, while the latter can be solved using enumerative algebraic geometry. Then, by studying the properties of so-called (G,q)-opers on a projective line I will connect the two types of integrable models. In the end, some applications of opers to other fields of mathematics like cluster algebras, symplectic duality, etc will be discussed.

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