Seminars & Colloquia Calendar
Hitchin connection on Teichmueller curves and quantum pseudo-Anosovs
Shehryar Sikander ICTP
Location: Serin E371
Date & time: Thursday, 09 May 2019 at 1:00PM - 2:00PM
Implicit in the construction of the Witten-Reshetikin-Turaev TQFT are quantum representations of mapping class groups of genus g surfaces. Geometrically, these representations are given by the monodromy of the Hitchin connection on the moduli space of curves. Teichmueller curves are totally geodesic algebraic curves contained in the moduli space of curves. We study the restriction of the Hitchin connection to these curves. This has two
advantages: The monodromy computation of the restricted connection is much easier as we are on a curve and the totally geodesic property implies that this monodromy contains quantum representations of infinitely many pseudo-Anosov elements. We will present an explicit computation of the monodromy of the Hitchin connection restricted to a particular Teichmueller curve contained in the moduli space of genus two curves.