Positivity, higher Teichmüller spaces and (non-commutative) cluster algebras

https://hu-berlin.zoom.us/j/61339297016
 

Higher Teichmüller theory emerged as a new field in mathematics about twenty years ago. It generalizes Thurston’s view on Teichmüller space, but also draws on new connections to representation theory, Higgs bundles, theoretical physics and cluster algebras. In this talk I will provide an overview of the different approaches to higher Teichmüller spaces, and explain how a generalization of total positivity provides a (conjectural) unifying framework. It also leads to new predictions and connections to  Lie groups over non-commutative rings.