In my talk I will explain the recent progress on the multidimensional Borg-Levinson theorem since the founding paper by Nachman, Sylvester and Uhlmann (1988). I will specifically show how to recover a Schrodinger operator from boundary spectral data. I will present various uniqueness and stability results. The most recent result I will present concern the magnetic Laplace-Beltrami operator. In that  case we want to retrieve both the magnetic and electric potentials from boundary spectral data.

Mourad Choulli is full professor at University of Lorraine since 1998. Before he was assistant professor in 1988 and associate professor from 1989 to 1998 at University of Franche-Comte. From 1998 to 2008 he was the head of "Analysis and PDEs" group at the department of mathematics of University of Lorraine. He obtained his PhD degree from University of Toulouse in 1987 and his "habilitation" degree from University of Franche-Comte in 1996. His research focuses on mathematical analysis of inverse problems for PDEs, inverse spectral theory and Gaussian bounds for fundamental solutions and Green's functions.