For more information about this meeting, contact Dmitri Burago, Anatole Katok, Aaron Brown.
|Title:||On discretization in Riemannian Geometry|
|Seminar:||Center for Dynamics and Geometry Seminars|
|Speaker:||Dima Burago, Penn State|
|Traditionally, discretization in Riemannian geometry was associated with polyhedral approximations. It seems now clear, due to works of Cheeger, Petrunin, Panov and many others that in dimensions beyond two or maybe three polyhedral structures are too rigid and cannot serve as discrete models of Riemannian spaces. Of course, there are various finite element methods, they do help to solve PDEs but they seem to be just numerical methods not helping us to understand underlying geometry and make models. They also seem to be confined to regions in Euclidean spaces.
In this talk, we will discuss approximating Riemannian manifolds by graphs, of course with additional structures attached to them and with various boundedness conditions. We will discuss both metric and PDE aspects, including a comparison of spectral characteristics of the graph and smooth Laplacians. The talk is based on a joint work with S. Ivanov and (the latter part) with S. Kurylev.|
Room Reservation Information
|Date:||09 / 12 / 2012|
|Time:||03:35pm - 05:30pm|