Speaker: Zhengjiang Lin (MIT)

Title: Asymptotic topological statistics of Gaussian random zero sets of codimensions ≥ 1.

Abstract:

We will briefly discuss some asymptotic topological statistics of zero sets of Gaussian random waves, which can have codimensions greater than 1. This includes a special case on random distributions of knots as the zero sets of complex arithmetic random waves. We will also discuss some results on zero sets of Gaussian band-limited functions consisting of Laplacian eigenfunctions, which are related to Courant’s nodal domain theorem and Milnor-Thom’s theorem on Betti numbers of real algebraic varieties.