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#### Modern Mathematics Lecture Series Representation theory and a little bit of quantum field theory

Abstract：One of the central foci of representation theory in the 20th century was the representation theory of Lie algebras, starting with finite dimensional algebras and expanding to a rich, but still mysterious infinite dimensional theory. In this century, we realized that this was only one special case of a bigger theory, with new sources of interesting non-commutative algebras whose repres...

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#### Modern Mathematics Lecture Series | Dynamics on character varieties and Hodge theory

AbstractLet X_n be the set of tuples of 2x2 matrices (A_1, A_2, ..., A_n) such that the product A_1...A_n is the identity matrix, and considered up to simultaneous conjugation. On each X_n, there is a very classical and explicit action of the so-called braid group B_n. This is an elementary case of the so-called mapping class group action on the character varieties of surface groups, and was st...

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