Noncommutative Surfaces

by Jens Hoppe (Sogang Univ.)

Wednesday 5 Feb 2014, 14:30 → 16:00 Europe/Berlin

Sem Raum 2 (DESY Hamburg)

Many aspects of the differential geometry of embedded Riemannian manifolds, including curvature, can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. For matrix analogues of embedded surfaces, one can define discrete curvature, and a noncommutative Gauss-Bonnet theorem. After giving a general introduction to the Poisson-algebraic reformulation for surfaces, as well as explaining a method to associate sequences of finite dimensional matrices to them, I will focus on concrete examples, including noncommutative analogues of minimal surfaces ( that play a central role in one of the more promising attempts to unify the known physical interactions).