Mathematical Physics and Harmonic Analysis Seminar

Date: October 5, 2018

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Lior Alon, Technion --- Israel Institute of Technology

Title: Nodal and Neumann count statistics for quantum graphs

Abstract: In this talk I will briefly go over the definitions and results from the work on the nodal count statistics on quantum graphs. Then I will introduce the concept of Neumann count, and properties of Neumann domains such as the spectral position of the restricted eigenfunction and analogous property to the area to length ratio (isoperimetric parameter). I will then state the results regarding the existence and symmetry of the probability distributions of the latter properties.

If time allows I will present a simple but powerful result regarding the edge lengths dependence of the nodal and Neumann distributions for edge transitive combinatorial graphs, and I will finish with our latest results, showing that the nodal distributions for two specific graphs families converge to Gaussian distributions as the the number of edges grows to infinity.

This talk is base on a joint work with R. Band (Technion) and G. Berkolaiko (Texas A&M).