Abstract: 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, and spectral theory. In my talk, I will discuss possible extensions of this theory to the setting of graphs. It is a fairly new topic and most of the results in the area are proved in the last two years. 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, and will be based on a joint work with Stefan Steinerberger.
