Correlation inequalities for the Tutte polynomial
Discrete Structures and Algorithms (Seminar)
The speaker is a DECRA Fellow who recently commenced work in our department.
by Dr Arun Mani
Abstract: In this second of the two part talk, I will introduce a family of correlation inequalities for the Tutte polynomial of a graph. I will discuss how this arises naturally from fundamental combinatorial questions on a graph. I will then talk about the following topics of my research on these inequalities:
i) theoretical tools to establish these inequalities,
ii) applying the inequalities to obtain approximations for the Potts model partition function in Statistical Mechanics, and
iii) their potential as a general approximation technique for the Tutte polynomial.
Along the way, we will see that there are several interesting fundamental questions on the topic that are still unresolved and very much wide open for further research.