Time | Speaker | Title | Resources | |
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09:45 to 10:45 | Michael Wheeler (University of Melbourne, Australia) |
Colored vertex models - II TBA |
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11:30 to 12:20 | Guillaume Barraquand (CNRS, France) |
Stationary measures for integrable probabilistic systems We will present a method for computing the stationary measures of integrable probabilistic systems on finite domains. Focusing on the example of a well-studied model called last passage percolation, we will describe the stationary measure in various ways, and emphasize the key role played by Schur symmetric functions. The method works as well for other models and their associated families of symmetric functions, suchas Whittaker functions or Hall-Littlewood polynomials. We will also discuss how this is related to the traditional approach for computing stationary measures of interacting particle systems between boundary reservoirs: the matrix product ansatz. |
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12:30 to 12:50 | Sudeshna Bhattacharjee (IISc, India) |
Law of Fractional Logarithms for Extrema of Airy Processes Airy_1 and Airy_2 processes are stationary stochastic processes on the real line that arise in various contexts in integrable probability. In particular, they are obtained as scaling limits of passage time profiles in planar exponential last passage percolation (LPP) models with different initial conditions. In this talk, we shall present law of fractional logarithms with optimal constants for maxima and minima of Airy processes over growing intervals, extending and complementing the work of Pu. We draw upon the recently established sharp tail estimates for various passage times in exponential LPP by Baslingker et al., as well as geometric properties of exponential LPP landscape. The talk is based on a recent work with Riddhipratim Basu |
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14:30 to 14:50 | Takuya Inoue (University of Tokyo, Japan) |
New signed bijections pertaining to alternating sign matrices and Gelfand-Tsetlin patterns Alternating sign matrices (ASM) and descending plane partitions (DPP) both have the concept of rank, and it has been known that the same number of them exist for each rank (conjectured in 1983 by W. H. Mills, David P. Robbins and Howard Rumsey, Jr., and proved in 1996 by Doron Zeilberger and by Greg Kuperberg independently). However, no explicit bijections between them have been found so far. This problem is known as the ASM-DPP bijection problem. In 2020, Fischer and Konvalinka constructed a bijection between ASM(n)xDPP(n-1) and ASM(n-1)xDPP(n), where ASM(n) denotes the set of ASMs with rank n, and it is similar for DPP(n). This bijection was developed using the concept of signed bijections. I introduce the notion of compatibility of signed bijections to measure the naturalness of signed bijections and to simplify the construction. In this talk, I present the definition of compatibility and some of the results obtained from it. For example, these include the refined structure of Gelfand-Tsetlin patterns and some simplified signed bijections related to ASMs. |
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14:55 to 15:15 | David Whiting (Michigan State University, USA) |
Embeddings of generalized cluster algebras A notion of generalized cluster algebras was introduced by L.Chekhov and M.Shapiro, where the exchange relations are given by polynomials of arbitrary order. A natural question arises; can these generalized cluster algebras be embedded into some standard cluster algebra? In a joint work in progress with R.Ramos, we provide a construction and show that the answer is yes. In this talk, I will briefly describe what a generalized cluster algebra is, and provide a few examples of this embedding. |
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15:20 to 15:40 | James Beyer (Oklahoma University, USA) |
Deep Points of Algebras from Marked Surfaces In this talk, we consider the skein algebra (or cluster algebra) of an oriented marked surface with boundary. Each triangulation of the surface determines an algebraic torus in the corresponding variety, and in some cases these tori collectively cover the variety. In other cases, there are points not contained in any algebraic torus, which we call deep points. In joint work with Greg Muller, we have classified the deep points of skein algebras of unpunctured marked surfaces. We will discuss this classification, beginning with convex polygons and then extending those same ideas to other unpunctured surfaces. |
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16:15 to 16:35 | Tista Banerjee (IACS, India) |
Entanglement transitions in non-Hermitian integrable Floquet systems In this talk I will try to describe how the interplay between the system environment coupling and external driving frequency shapes the dynamical properties and steady state behavior in a periodically driven transverse field Ising chain subject to measurement. I will describe fate of the steady state entanglement scaling properties as a result of measurement induced phase transition. I will briefly explain how such steady state entanglement scaling can be exactly computed using asymptotic analysis of the determinant of associated correlation matrix which turned out to be of block Toeplitz form. I will try to point out the differences from the Hermitian systems in understanding entanglement scaling behaviour in regimes where the asymptotic analysis can be performed using Fisher-Hartwig conjecture. I will end the talk with some open questions in this direction. |
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16:40 to 17:00 | Peter Leach (University of Kwazulu-Natal, South Africa) |
Solutions of Magnetohydrodynamics Equation through Symmetries The magnetohydrodynamics (1 + 1) dimension equation, with a force and force-free term, is analysed with respect to its point symmetries. Interestingly, it reduces to an Abel’s Equation of the second kind and, under certain conditions, to equations specified in Gambier’s family. The symmetry analysis for the force-free term leads to Euler’s Equation and to a system of reduced second-order odes for which singularity analysis is performed to determine their integrability. |