Fatkullin: Statistical mechanics of graphs and partitions

The term "statistical mechanics" is most commonly associated with physics of gases or liquids. Even though this has been the case historically, in the present time, methods of statistical mechanics have expanded well beyond their original scope. In this talk I will discuss several (deceptively) simple examples from everyday life which lead to exciting stat. mech. models such as random graphs and partitions. Lots of the associated problems are very easy to formulate, but not-so-easy to solve, and have deep connections to seemingly unrelated fields such as representation or spectral theories.