**Peter Sarnak **(Princeton)

*Topologies of nodal sets of random band limited functions** *

**Abstract:** We discuss various Gaussian
ensembles for real homogeneous polynomials in several variables
and the question of the distribution of the topologies of the
connected components of the zero sets of a typical such random real
hypersurface. For the "real -Fubini -Study ensemble" and at other
end the "monochromatic wave ensemble", one can show that these
have universal laws. Some qualitative features of these laws are
also established.

Joint work with I.Wigman.