Gupta: Discrete rearrangement inequalities on graphs

In the Euclidean space setting, rearrangement inequalities is a classical theory that has been quite useful in solving problems coming from various parts of analysis: spectral geometry, variational problems, mathematical physics, spectral theory, to name a few. In my talk, I will discuss a possible extensions of this theory to the setting of discrete graphs. It is a fairly new topic and very few results are known so far. I will talk about these developments, connections of this theory with discrete isoperimetric inequalities, and its possible applications to problems concerning ‘analysis on graphs’. The talk will be at the interface of discrete math and analysis.