Painlevé VI, dynamics, and beyond
Painlevé VI, dynamics, and beyond
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Peter Whang, Princeton University
We begin by discussing the Painlevé VI equation, a nonlinear secondÌýorder ordinary differential equation discovered by R. Fuchs (1906),Ìýwhich has several beautiful properties and applications. We describeÌýhow the classification of its algebraic solutions, completed byÌýLisovyy-Tykhyy (2008), connects to mapping class group dynamics of theÌýfour punctured sphere on certain moduli spaces. Time permitting, weÌýpresent an analogous classification in mapping class group dynamicsÌýfor higher genus surfaces (which turns out to be much simpler), andÌýdiscuss open conjectures.