Eric Carlen, Rutgers University

Abstract

We consider a class of graphs describing a system of N particles with r prescribed energy levels that interact through pair "collisions" in which they exchange energies. In the mathematical physics problem associated to this model, the spectral gap of the graph Laplacian on the connected components is of interest. We present a simple method for determining the exact spectral gaps in all cases and all of the gap eigenfunctions. The method also yields some additional information on the spectrum. We discuss some conjectures supported by Maple computations.

This is joint work with Michael Loss.

Link to video: https://vimeo.com/704252776

Presented Via Zoom: https://rutgers.zoom.us/j/94346444480

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/