Jeff Kuan
The Ohio State University
Title
Probability Seminar: Quantum Groups, Interacting Particle Systems, and Writing a Paper with GenAI
Abstract
The Type D asymmetric simple exclusion process (ASEP) is a two-species interacting particle system in which neither species has priority over the other, and both the orthogonal polynomial duality function and the reversible measures factor over the two species. This suggests that the Type D ASEP converges to two independent copies of the KPZ equation, with asymptotic fluctuations given by two independent Tracy-Widom distributions. The generator of the Type D ASEP arises from central elements of the quantum groups U_q(so_{2n}), where the rank n controls the drift speed rather than the number of species. In this talk, I give an overview of the construction and describe how a sequence of undergraduate research projects — and most recently a generative AI coauthor — have computed these central elements for increasingly large n. The talk will emphasize the probabilistic motivation and open questions, including conjectural extensions to exceptional Lie algebras.