Speaker: B. Bychkov (Higher School of Economics, Moscow)
Date and time: 3.06.2020, 18:00 (GMT +03:00)
Title: Star-triangle transformation of the Potts model partition function as a solution for the tetrahedron equation and related combinatorial topics
Abstract: The report is devoted to several well-known functional relations in the theory of polynomial graph invariants, as well as some new interpretations. The identification of Tutte polynomials with partition functions of the Potts-type models seems to be an ideal possibility to apply the methods from the theory of integrable models of statistical physics to the combinatorics of graphs and vice versa.
I will present at least one proof of the fact that the parameter transformation, defining the invariance of the n=2 Potts model partition function under the star-triangle transformation, gives an orthogonal solution for the local Yang-Baxter equation and for the tetrahedron equation.
Using the Biggs duality on the space of Potts model partition functions I will present several results about the connection between the chromatic and flow polynomials and as a consequence obtain shifting order formulas on the space of Potts model partition functions.
The talk is based on the recent joint work with A.Kazakov and D.Talalaev.
To access the online seminar please contact Anna Tolbey firstname.lastname@example.org