Speaker: Anton Dzhamay (BIMSA)
Time: 2025-12-18 14:00-16:00
Location: 1710, SIMIS
Zoom Meeting ID: 812 4129 2242 Passcode: SIMIS
摘要：
Discrete Painlevé equations are a class of important second-order nonlinear recurrencies that correspond to bilinear representations of some affine Weyl groups. They appear in many importat questions in Mathematical Physic, in particular, in the theory of Orthogonal Polynomials and in Integrable Probability. The name reflects the fact the some of these recurrencies have continuous limit to the usual (differential) Painlevé equations, which resulted in the original naming convention, such as d-PII or alt-d-PII. This was later changed to the Sakai classification scheme that, on one hand, describes allpossible configuration spaces for such discete dynamics and, on the other hand, explains how symmetry groups of the configuration spaces can be used to generate the dynamics. The commonbelief is that these two notions are interchangeable. However, that is not the case — some discrete Painlevé dynamics are restricted to proper loci in generic surface families whose symmetry groups generate the dynamic. In this talk we illustrate this using a specific and well-known example of a d-PII equation, and some of its further specializations appearing in the computation of gap probabilities of the Freud unitary ensemple.
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