**Professor Vladimir Sharafutdinov**

Sobolev Institute of Mathematics, Novosibirsk, Russia

**"Spectral and Boundary Rigidity of Riemannian Manifolds"**

**Abstract:**

Vladimir Sharafutdinov received his PhD from the Novosibirsk State University, 1974, and second doctoral degree from the Institute of Mathematics, Novosibirsk in 1990. Since there he holds research and teaching positions at these institutions. His main research field is Riemannian and integral geometry where he published several papers and a book. In his lecture he will discuss the following topic:

Boundary rigidity problem is posed as follows: to what extent is a Riemannian metric on a compact manifold with boundary determined by distances between boundary points? The corresponding Riemannian manifold is called boundary rigid if the metric is determined uniquely up to an isometry identical on the boundary. There is the corresponding definition of deformation boundary rigidity when we are interesting in continuous deformations of metrics. There is also the periodical version of the problem of recovering a metric on a closed boundaryless manifold from given lengths of closed geodesics. The latter problem relates closely to inverse problem of recovering geometry of a closed Riemannian manifold from the spectrum of the Laplace - Beltrami operator.

#### Friday, October 16, 1998

3:00 PM in 335 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Fall 1998]