Seminars & Colloquia Calendar
NON-COMMUTATIVE COORDINATES FOR MAXIMAL SYMPLECTIC REPRESENTATIONS
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.