RTG Seminar on Geometry, Dynamics and Topology Seminar

Shear and lambda-lengths coordinates parametrize two different versions of the Teichmueller space of a surface S with boundary and marked points.

Fock and Goncharov greatly generalized this picture by connecting it to Lusztig's theory of total positivity. Among other things, they introduced two new (dual) Higher Teichmueller spaces for S, and they proved that each of these spaces admits a ``positive part''. Moreover, they parametrized these positive parts using coordinates for moduli spaces of flags. The coordinate changes are explicitly described using tools coming from cluster algebras.

This series of talks will start by recalling the classical examples in an easy-to-generalize framework. As a consequence, very little background will be needed. Speaker(s): Giuseppe Martone (U Michigan)