Topologies of nodal sets of random band limited functions

The next Mathematical Colloquium will take place on 
December 30, 2018 [Sunday] @15:00. 

Prof. Igor Wigman (King's College London, UK) will give a talk on “Topologies of nodal sets of random band limited functions”.

Abstract

We are interested in the nodal structures (namely, the zero set) of  important Gaussian ensembles of random functions. In many situations the powerful techniques of Nazarov-Sodin yield the asymptotic behaviour of  the total expected number of nodal domains (or components). We show that their topologies and nestings of the zero and nodal sets of random (Gaussian) band limited functions have universal laws of  distribution.

Qualitative features of the supports of these distributions will be determined. In particular the results apply to random monochromatic waves and to random real algebraic hyper-surfaces in projective space.

This talk is based on a joint work with Peter Sarnak.

Place: Holon Institute of Technology, Faculty of Sciences, Room 424/8.

(Light refreshments will be served at 14:45)

Everybody is welcome.