Two talks Monday Nov 14, 2-4pm Fields 210

[Benjamin Landon]

Hi all,

Tomorrow we will have two talks, both in Fields 210.  Tomas Dominguez Chiozza will speak from 2:10-3:00 and then  Nishant Chandgotia will speak from 3:10-4:00pm. Titles and abstracts are below.

2-3pm

Speaker:  Tomas Dominguez Chiozza

Title: Mutual information for the sparse stochastic block model

 Abstract: In this talk, we consider the problem of recovering the community structure in the stochastic block model with two communities. We aim to describe the mutual information between the observed network and the actual community structure in the sparse regime, where the total number of nodes diverges while the average degree of a given node remains bounded. The main result will be a conjecture for the limit of this quantity, and a proof that this conjectured limit provides a lower bound for the asymptotic mutual information. In the case when links across communities are more likely than links within communities, the asymptotic mutual information is known to be given by a variational formula. We also show that our conjectured limit coincides with this formula in this case. This is based on joint work with Jean-Christophe Mourrat.

3-4pm

Speaker:  Nishant Chandgotia

Title: The Dimer Model in 3 dimensions

Abstract: The dimer model, also referred to as domino tilings or perfect matching, are tilings of the Z^d lattice by boxes exactly one of whose sides has length 2 and the rest have length 1. This is a very well-studied statistical physics model in two dimensions with many tools like height functions and Kasteleyn determinant representation coming to its aid. The higher dimensional picture is a little daunting because most of these tools are limited to two dimensions. In this talk I will describe what techniques can be extended to higher dimensions and give a brief account of a large deviations principle for dimer tilings in three dimensions that we prove analogous to the results by Cohn, Kenyon and Propp (2000).