Non commutative cluster coordinates for Higher Teichmüller Spaces

Geometry & Topology
Event time: 
Tuesday, February 4, 2020 - 4:15pm
DL 431
Daniele Alessandrini
Speaker affiliation: 
Columbia University
Event description: 

Fock-Goncharov found a beautiful structure of cluster
variety on the decorated Hitchin components of punctured surfaces,
generalizing Penner's decorated Teichmüller Theory. This is an
algebraic theory based on the notion of positivity.
Hitchin components are an example of Higher Teichmüller Spaces, and
the spaces of Maximal Representations are another example. In this
latter case, we found new coordinates on these Higher Teichmüller
Spaces that give them a structure of non-commutative cluster
varieties, in the sense defined by Berenstein-Rethak. This is joint
work with Guichard, Rogozinnikov and Wienhard.

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