Closure of Orbits of the Pure Mapping Class Group on the Character Variety

Explore the intricate dynamics of the pure mapping class group's action on the character variety in this advanced mathematics seminar. Delve into recent contributions to the theory, including an almost complete description of Zariski-closure for infinite orbits in characteristic zero fields, insights into SU(2)-representation orbit closures for n-puncture spheres, and a precise analysis of orbit closures in p-adic integer points. Gain a deeper understanding of the connections between this action and algebraic solutions to Painleve differential equations, as well as the historical context of Goldman's work on SU(2)-representations. Examine the limitations of previous results by Previte and Xia, and discover the exceptional cases in p-adic settings. This joint work with Natallie Tamam builds upon and extends seminal research in the field, offering new perspectives on the closure of orbits in various mathematical contexts.