Event Type:

Seminar

Date/Time:

Monday, January 9, 2006 - 07:00

Location:

Kidder 280

Guest Speaker:

Vladimir Sharafutdinov

Abstract:

For a compact Riemannian manifold (M,g) with boundary, we define the Dirichlet to Neumann (DN) operator on exterior differential form of arbitrary degree. It coincides with the classical DN map on forms of zero degree. How far are the topology and geometry of the manifold determined by the DN operator? We prove that all Betti numbers can be recovered and present an explicit formula expressing Betti numbers in terms of the DN map.