Nattalie Tamam

Imperial Imperial


Closure of orbits of the pure mapping class group in the character variety


Ergodic Theory and Dynamical Systems Seminar


20th February 2025, 2:00 pm – 3:00 pm
Fry Building, 2.04


The pure mapping class group of an oriented surface acts on the character variety of the surface. For certain surfaces, such orbits are connected to solutions of known problems, such as the Markoff triples and the sixth Painlevé equation. We will discuss these examples, as well as the possible orbits closure in the general case; the algebraic relations preserved under the action, the obstructions to 'big' orbits, and the exceptional cases. This is a joint work with Alireza Salehi-Golsefidy.






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