Mathematics Colloquia and Seminars

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After a brief introduction to character varieties we will discuss their complete integrability. It is known that the trace functions of a maximal set of disjoint simple closed curves on a closed surface make its SL(2,C)-character variety into a completely integrable dynamical system and, hence, lead to a system of action-angle coordinates. We prove an analogous statement for rank 2 Lie groups. Time permitting we will discuss the application of this result to quantization of character varieties.