Positivity, Representations, and Non-Commutative Hyperbolic Geometry

Explore the concept of total positivity in matrices and its generalization to split real Lie groups in this mathematics colloquium talk by Anna Wienhard from Heidelberg University. Delve into Lusztig's notion of positivity in flag varieties and its role in Fock and Goncharov's work on higher Teichmüller spaces. Discover a new, more comprehensive definition of positivity in flag varieties that extends beyond Lusztig's original concept. Examine the applications of this novel approach to higher Teichmüller spaces and investigate the geometric and dynamical properties of surface group representations. Gain insights into the interconnections between positivity, representations, and non-commutative hyperbolic geometry in this hour-long presentation from the Stony Brook Mathematics Colloquium.