Event time:

Tuesday, February 4, 2020 - 4:15pm

Location:

DL 431

Speaker:

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.

Research Area(s):