Rinat Kashaev

"Symmetrically factorized Lie groups and representations of the groupoid
of ideal triangulations of a punctured surface"

Abstract: Groupoid of ideal triangulations of a punctured surface of finite type
is a category with objects given by $Diff_+$ (orientation preserving
diffeomorphisms) classes of ideal triangulations of the surface and morphisms
being $Diff_+$ classes of pairs of ideal triangulations with respect to diagonal
action of $Diff_+$. I will discuss a construction of representations of this
groupoid by using a Lie group $G$ admitting a symmetric factorization, i.e. with
two conjugate subgroups $G_\pm$ such that they intersect trivially and the subset
$G_+G_-$ is dense in $G$.