Topologies of nodal sets of random band limited functions

Members' Seminar
Topic:Topologies of nodal sets of random band limited functions
Speaker:Peter Sarnak
Affiliation:Professor, School of Mathematics
Date:Monday, March 3
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/members/2014/0303-PeterSarnak

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 the 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.