Title:  Discrete spherical and hyperbolic Laplacians

Speaker:  Ivan Izmestiev

Abstract: The so-called cotangent Laplacian is a symmetric negative semidefinite matrix associated with a Delaunay triangulation of a point set in the plane. It has many applications in discrete differential geometry and is an indispensable tool in computer graphics.

In this talk I will describe a similar discretization of the spherical and hyperbolic Laplacians. It associates a negative semidefinite self-adjoint operator to a point set in the unit sphere or, respectively, in the hyperbolic plane. These discrete Laplacians share many properties with their classical smooth counterparts, in particular they are related to (discrete) conformal vector fields.

This is a joint work with Wai Yeung Lam.