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1-parameter families of compact Riemann surfaces

Shehryar Sikander
(QGM/Math, Aarhus University)
Torsdag, 26 juni, 2014, at 11:15-12:15, in Aud. D1 (1531-113)
We introduce a (complex) one parameter family of compact Riemann surfaces and study an ordinary differential equation of Fuchsian type on this parameter space. We present the solution of this equation in terms of iterated integrals. We then show how this ODE is related to the Hitchin connection over this parameter space, and how the solutions give the monodromy for the Hitchin connection. This relation with Hitchin connection relies on the fact that the parameter space is a Teichmueller curve. This is joint with J. E. Andersen and N. L. Gammelgaard.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen