Hodge theory, braid groups, and some questions about 2x2 matrices

Abstract: Let $X_n$ be the set of conjugacy classes of n-tuples of 2x2 matrices whose product is the identity matrix--equivalently, the character variety of a n-punctured sphere. There is a natural braid group action on $X_n$, whose study goes back to work of Markoff in the late 19th century. The most basic question one can ask about this action, which dates to work of Painlevé, Fuchs, Schlesinger, and Garnier in the beginning of the 20th century, is: what are the finite orbits? I'll explain the history of this question, as well as some recent work, joint with Lam and Landesman, in which we give a complete classification of such finite orbits, by algebro-geometric methods, when at least one of the matrices in question has infinite order.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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