The Mathematical Physics and Probability seminar will be running during Autumn 2020 on Tuesdays at 1pm via zoom (link to be provided via email). The topic will be on Hecke Algebras and applications to integrable probability.
20/10 Oleg Zaboronski
Title: Reaction-diffusion, exclusion models and Hecke algebras - notes
Let us consider a class of interacting particle systems on Z, which have a generator
are linear operator, which only act on sites
. As it turns out, one can construct a full set of duality functions for such a model, provided g_i's generate Hecke algebra. The models singled out by this condition include ASEP, symmetric annihilating coalescing random walks, branching-coalescing random walks, annihilating random walks with immigration. Will the knowledge of representation theory prove useful in studying these models?
27/10 Oleg Zaboronski
Title: Reaction-diffusion, exclusion models and Hecke algebras: Part II.
Below is some preliminary reference list. This list will be updated and refined based on the material and topic that we will decide to focus on.
A.P. Isaev, O.V. Ogievetsky