Mathematics Department Colloquium: Non-commutative hyperbolic geometry

Colloquium | October 3 | 4:10-5 p.m. | 60 Evans Hall

 Anna Wienhard, Universität Heidelberg

 Department of Mathematics

Hyperbolic geometry and, in particular, the study of hyperbolic structures on surfaces is a very rich topic, that has connections to many areas in mathematics. After giving a short introduction into some of its aspects, I will show that there is a related story of non-commutative hyperbolic structures on surfaces, in which the symplectic group, maximal representations and non-commutative cluster algebra play a role. This all fits into a more general (partially conjectural) framework involving generalizations of total positivity, that I will discuss in the end.