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...

Polynomial optimization concerns minimizing a polynomial subject to polynomial equations and inequalities. While this is a natural model for many applications, there are many difficulties (usually numerical and algorithmic) that have prevented their...

Many results in extremal graph theory can be formulated as inequalities on graph densities. While many inequalities are known,many more are conjectured. A standard tool to establish an inequality is to write the expression whose nonnegativity needs...