Bounds on sums of graph eigenvalues

Math Physics Seminar
Friday, February 1, 2013 - 16:00
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
I'll discuss two methods for finding bounds on sums of graph eigenvalues (variously for the Laplacian, the renormalized Laplacian, or the adjacency matrix). One of these relies on a Chebyshev-type estimate of the statistics of a subsample of an ordered sequence, and the other is an adaptation of a variational argument used by P. Kröger for Neumann Laplacians.  Some of the inequalities are sharp in suitable senses.  This is ongoing work with J. Stubbe of EPFL