# Will Perkins “Counting independent sets with the cluster expansion”

May 14, 2020
19.00 MSK (UTC +3)

# Will Perkins "Counting independent sets with the cluster expansion"

Will Perkins from University of Illinois at Chicago will give the talk "Counting independent sets with the cluster expansion" on the labs' Big Seminar.

The talk will be held in zoom
Meeting ID: 279-059-822
Password: First six digits of $\pi$ after the decimal point

You can also write to Alexander Polyanskii (alexander.polyanskii@yandex.ru) or to Maksim Zhukovskii (zhukmax@gmail.com) if you want to be added to mailing list.

Abstract:

I'll present two tools from statistical physics, abstract polymer models and the cluster expansion, and show how they can be used in extremal and enumerative combinatorics to give very good approximations to the number of (weighted) independent sets in certain graphs. In one application we use the cluster expansion in concert with Sapozhenko's container lemma (and Galvin's generalization) to obtain new results on the weighted number of independent sets in the hypercube and their typical structure. Joint work with Matthew Jenssen.

Slides

## Watch the lecture on youtube:

Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.