Classical marginal problem is about existence of a ``body" = probability density in $\Bbb R^n$ with given projections onto some coordinate subspaces. Its quantum version was known in physics as {\it $N$ representability problem} from early 60s. Later on in 1995 it was designated as one of 10 most prominent research challenges in quantum chemistry. The problem includes as a very special case description of relations between spectra of Riemann and Ricci curvature tensors.In the talk I'll discuss recent progress in this problem based on Geometric Invariant Theory, and its connection with longstanding problems representations of compact groups.

Alexander Klyachko

General Seminar, 21.04.2005