Thursday, September 19, 2019
Time  Items 

All day 

3pm 
09/19/2019  3:00pm Associated to a convex integral polygon $P$ is a dimer cluster integrable system $\mathcal X_P$ of Goncharov and Kenyon. We compute the cluster modular group $G_P$ of $\mathcal X_P$. Probabilistically, nontorsion elements of $G_P$ correspond to ways of shuffling the underlying bipartite graph, generalizing the domino shuffling algorithm. Location:
DL 316

4pm 
09/19/2019  4:00pm Abtract: In 1970, Hoffman gave a spectral upper bound on the size of an independent set of a graph. Since then it found applications and generalizations in different fields. In particular, the original bound and its generalization to hypergraphs became a powerful tool in extreme combinatorics by providing a spectral proof to a number of problems, e.g., ErdosKoRado, DezaFrankl, Mantel Theorems, and others. The usual approach is to show that an explicit family of objects is extreme by showing that its size achieves the Hoffman bound in the (hyper)graph of constraints. It turns out that these examples of independent sets in graphs are also extreme for the question of sampling on graphs posed recently by Steinerberger. If time permits, I’ll also talk about the spectral approach to independent sets on the hyperbolic plane and its quotients. Location:
LOM 215
