UW Combinatorics and Geometry Seminar: Rekha Thomas

An unweighted graph is conformally rigid if allowing nonnegative edge weights will not increase the second eigenvalue, or decrease the largest eigenvalue, of its Laplacian matrix. There are natural motivations for finding weights on a graph that maximizes/minimizes these eigenvalues. At first glance, conformal rigidity appears to mandate a great deal of symmetry. In this talk we will see several nontrivial graphs (and graph families) that are conformally rigid. The techniques involve semidefinite programming and some symmetry reduction. (Joint work with Stefan Steinerberger.)