### Fully discrete two dimensional equations of Liouville type

Kashaev, R *(Geneva)*

Tuesday 24 March 2009, 10:00-11:00

Meeting Room 3, CMS

#### Abstract

It is known that the Discrete Liouville equation with periodic boundary conditions of length N can be formulated within Teichmoeller theory as an evolution system corresponding to an "N-root" of a Dehn twist. One of the consequences of this interpretation is a geometrical explanation of the zero modes and their simple dynamics. In this talk I will discuss discrete equations the same geometric origin but associated with other representations of the mapping class groups of punctured surfaces.