01

Organizers

陈伟彦、高鸿灏、黄意、林剑锋

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Speaker

Peter Smillie (MPI Leipzig)

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Time

Thur., 16:00-17:00, Sept. 12, 2024

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Venue

B725, Shuangqing Complex Building A

清华大学双清综合楼A座 B725报告厅

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Online

Zoom Meeting ID: 405 416 0815

Password: 111111

The mapping class group action on SL(2,R) representations

Let X(G) be the character variety of representations of a surface group into a Lie group G, so that the mapping class group acts on X(G). When G is compact, this action is ergodic by work of Goldman and Pickrell-Xia, and a well-known conjecture of Goldman is that for G=PSL(2,R) (and genus at least 3), the action is ergodic on each non-Fuchsian topological component of X(G). This turns out to be essentially equivalent to a conjecture of Bowditch that every non-elementary non-Fuchsian representation in X(PSL(2,R)) sends some simple closed curve loop to a non-hyperbolic element. By studying the action of the mapping class group on the tangent cone to the subvariety of nontrivial diagonal representations, we prove that Bowditch's condition holds in a neighborhood of the nontrivial diagonal representations in the Euler number zero component. This is joint work with James Farre and Martin Bobb.

/ Peter Smillie /

MPI Leipzig

I am a research group leader (W2) at the Max Planck Institute for Mathematics in the Sciences in Leipzig.

My research is in differential geometry, Teichmüller theory, and geometric structures. I am also interested in general relativity and other connections to physics.

Personal Homepage:

https://petersmillie.github.io/