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Mathematical Physics and Probability Reading seminar

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.

Schedule

20/10 Oleg Zaboronski

Title: Reaction-diffusion, exclusion models and Hecke algebras - notes

Abstract: Let us consider a class of interacting particle systems on Z, which have a generator L=\sum_i g_i, where g_iare linear operator, which only act on sites (i,i+1). 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.

References

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

Chen-de Gier-Wheeler

Borodin-Wheeler

P. Galashin

Kuniba-Mangazeev-Maruyama- Okado

Lascoux-Leclerc-Thibon

A. Lascoux

Bufetov