Seminar by Christian Zickert (University of Maryland)

Title: Fock-Goncharov coordinates for rank 2 Lie groups

2016.06.21 | Jane Jamshidi

Date Tue 28 Jun
Time 13:00 14:00
Location 1532-122 (Aud. G2)

Abstract

We discuss the higher Teichmuller space A_{G,S} defined by Fock and Goncharov. This space is defined for a punctured surface S with negative Euler characteristic, and a semisimple, simply connected Lie group G. There is a birational atlas on A_{G,S} with a chart for each ideal triangulation of S. Fock and Goncharov showed that the transition functions are positive, i.e. subtraction-free rational functions. We will show that when G has rank 2, the transition functions are given by explicit quiver mutations.

We discuss the higher Teichmuller space A_{G,S} defined by Fock and Goncharov. This space is defined for a punctured surface S with negative Euler characteristic, and a semisimple, simply connected Lie group G. There is a birational atlas on A_{G,S} with a chart for each ideal triangulation of S. Fock and Goncharov showed that the transition functions are positive, i.e. subtraction-free rational functions. We will show that when G has rank 2, the transition functions are given by explicit quiver mutations.

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