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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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#### Reflections on the Hodge Conjecture from an Arithmetic Geometer

Speaker James D. Lewis is Professor at University of Alberta. His current research interests are in regulators of (higher) algebraic cycles into Hodge cohomology theories (such as Beilinson's absolute Hodge cohomology). With his colleague Matt Kerr, together initially with Stefan Mueller-Stach, they provided over the course of 10 years an explicit description of the Beilinson-Bloch regulators i...

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