On the geometry of nodal domains for random eigenfunctions on compact surfaces Speaker(s): Suresh Eswarathasan
Abstract:
A classical result of R. Courant gives an upper bound for the count of nodal domains (connected components of the complement of where a function vanishes) for Dirichlet eigenfunctions on compact planar domains. This can be generalized to LaplaceBeltrami eigenfunctions on compact surfaces without boundary. When considering random linear combinations of eigenfunctions, one can make this count more precise and pose statistical questions on the geometries appearing amongst the nodal domains: what percentage have one hole? ten holes? what percentage have their boundary being tangent 100 times to a fixed nonzero vector field? The first 2025 minutes will give a survey on some fundamental results of NazarovSodin, SarnakWigman, and GayetWelschinger before presenting some joint works with I. Wigman (King's College London) and Matthew de CourcyIreland (École Polytechnique Fédérale de Lausanne) answering these questions in the last 2530 minutes. Date: 01/10/2020  1:30 pm
Series: Mathematical Physics
