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Geometry, Symmetry and Physics Seminar

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.

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