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Geometry, Symmetry and Physics Seminar



Location:  Serin E372B
Date & time: Thursday, 31 October 2019 at 11:00AM - 12:00PM

Representations of the fundamental group of an orientable surface

of finite type into a Hermitian type Lie group G with maximal Toledo

invariant are of particular interest in the Higher Teichmuller theory.

These representations were studied by M. Burger, A. Iozzi and A. Wienhard

and generalize Fuchsian representation of the fundamental group

of a surface into PSL(2;R). Moreover, maximal representations have

particularly nice properties, e.g. they are injective with discrete image

in G.  In my talk, I introduce the X-type coordinates on the decorated

space of maximal representations of the fundamental group of a punctured

surface into Sp(2n;R). These coordinates generalize the Fock-

Goncharov coordinates for representations into PSL(2;R). If time permits,

I will talk about how we can understand the topology of the

decorated space of maximal representations using these coordinates.

This is a joint work with D. Alessandrini, O. Guichard and A. Wienhard.

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