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Seminar by Shehryar Sikander (QGM)

Title: The Veech curve and Hitchin connection

2014.04.08 | Christine Dilling

Date Wed 28 May
Time 15:15 16:15
Location Aud D. 3


We give an explicit expression for the Hitchin connection on a Teichmueller curve. This Teichmueller curve was discovered by Veech and has been extensively studied by Lochak and McMullen. We then give an explicit formula, in terms of Hyeprlogarithms, for the monodromy representation of the orbifold fundamental group of this Teichmueller curve with respect to the Hitchin connection. This formula can be used to compute quantum invariants of a family of hyperbolic mapping tori. Time permitting, we will talk about the construction of cocycles  (for all positive integers k) using the parallel transport of the Hitchin connection over the ergodic geodesic flow in the unit tangent bundle of this Teichmueller curve. We show that the cocycle at k=1 coincides with the Kontsevich-Zorich cocycle. This is joint work with J. E. Andersen and N. L. Gammelgaard.