Topology, Algebraic Geometry, and Dynamics Seminar (TADS): String topology, integrable systems, and noncommutative geometry

Speaker:  Nick Rozenblyum, University of Chicago

Title:  String topology, integrable systems, and noncommutative geometry

Abstract:  A classical result of Goldman states that character variety of an oriented surface is asymplectic algebraic variety, and that the Goldman Lie algebra of free loops on the surface acts by Hamiltonian vector fields on the character variety. I will describe a vast generalization of these results, including to higher dimensional manifolds where the role of the Goldman Lie algebra is played by the Chas-Sullivan string bracket in the string topology of the manifold. These results follow from a general statement in noncommutative geometry. In addition to generalizing Goldman’s result to string topology, we obtain a number of other interesting consequences including the universal Hitchin system on a Riemann surface. This is joint work with Chris Brav.

Time:  Friday, April 14, 1:30pm – 2:30pm

Place:  Exploratory Hall, room 4208