Title: Cluster Poisson varieties and their applications

Speaker: A. Goncharov (Yale University)
 
link to recording:
https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=7e5eb501-88de-4b39-bc3e-afee00cba641

 
 link to previous talk: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=5590ebc6-66ca-4f0e-9550-afd4013db501
 
 Abstract:
 
Cluster Poisson varieties appear in many areas of Mathematics, e.g. Geometry, 
Representation Theory, Mathematical Physics. 

They share many common features, including:
*) Quantization, depending on any complex Planck constant. 
**) Canonical linear basis in the space of regular functions.
***) One can consider points of cluster varieties with values in positive real numbers or their tropical points. 

I will start from the simplest example: configuration of five cyclically ordered 
points on the projective line. 

Then I  will discuss  moduli spaces closely related to the character varieties. 
The latter parametrise maps of the fundamental group of a topological surface S to a split simple Lie group G, modulo conjugation. 
In this example the positive / tropical  points describe the 
Higher Teichmuller space / laminations related to the pair G,S.