BEGIN:VCALENDAR VERSION:2.0 PRODID:-//132.216.98.100//NONSGML kigkonsult.se iCalcreator 2.20.4// BEGIN:VEVENT UID:20260908T231534EDT-0381vNOuRZ@132.216.98.100 DTSTAMP:20260909T031534Z DESCRIPTION:Integrable systems\, exactly solvable models and algebras\n\nTh is concentration month will mainly be focused on four topics: (1) Box and ball systems\; (2) Multivariate polynomials and exactly solvable models\; (3) Reflection algebras\, the q-Onsager algebra\, the Heun-Askey-Wilson al gebra and integrable systems\; (4) Adelic Grassmanian\, τ function\, enume rative problems.\n\nBox and ball systems\n\nThe box-ball system (BBS) disc overed by Takahashi-Satsuma is one of the most basic ultradiscrete integra ble systems and can be discussed from various viewpoints such as crystal b ases of quantum algebras\, tropical geometry\, combinatorics\, and cellula r-automaton. In particular\, as a new perspective\, discussions and analyz es from probability theory and combinatorics are being actively conducted. The viewpoints of Pitman’s transformation in probability theory for discr ete integrable systems enable to consider the behavior of the random initi al state of the BBS. A workshop on BBS will provide an opportunity for dir ect discussions among researchers pursuing related work and will result in a strong push for this new development.\n\nMultivariate polynomials and e xactly solvable models\n\nHistorically\, a significant part of the theory of classical orthogonal polynomials was developed in connection with its r elevance for the solution of spectral problems in one-dimensional Mathemat ical Physics. More recently\, prominent bases for the algebra of symmetric polynomials have been identified as eigenstates of quantum integrable par ticle models on the line or on the circle. The plan is to bring together e xperts from areas characterized by a fruitful interplay between the modern theory of multivariate orthogonal polynomials and their applications rela ted to the study of quantum integrable particle systems\, algebraic and co ordinate Bethe Ansatz models\, integrable probability and random matrices\ , exactly solvable spin chains\, the combinatorics of symmetric functions\ , and (non)symmetric Macdonald polynomials (amongst others).\n\nReflection algebras\, the q-Onsager algebra\, the Heun-Askey-Wilson algebra and inte grable systems\n\nIn the context of quantum integrable systems\, Sklyanin’ s reflection algebras have played an important role in recent years. Since the 90’s K-matrix solutions of reflection algebras have been the basic bu ilding blocks for constructing transfer matrices and the associated quantu m spin chain Hamiltonians with integrable boundary conditions. The Bethe e quations and the underlying TQ relations of these open quantum systems hav e been studied extensively. However\, the interest in reflection algebras extends beyond this application: besides the fact that a complete classifi cation of universal K-matrices is an active field of research in mathemati cs\, it is now clear that reflection algebras provide an efficient framewo rk for studying the representation theory of the (Heun)-Askey-Wilson algeb ras\, q-Onsager algebra and its higher rank analogs. Also\, techniques suc h as the algebraic Bethe ansatz and its modified version can be used to ch aracterize the spectral properties of various operators emerging from thes e algebras. This is closely related with the subject of Leonard pairs and tridiagonal pairs and associated polynomial schemes. In particular\, it is expected that reflection algebras and K-matrices associated with higher r ank finite Lie algebras will naturally lead to generalizations of orthogon al polynomials. Also\, establishing the precise relationship between Bethe ansatz equations and the representation theory for these algebras is expe cted to provide new insight on multivariate orthogonal polynomials.\n\nAde lic Grassmanian\, τ function\, enumerative problems\n\nThe development of the theory of integrable systems is deeply tied with the geometry of Grass man manifolds since very early work of Sato\, Segal\, Wilson. In this cont ext the notion of Tau function appeared in origin as generating function o f commutative flows. Tau functions can be considered as a far-reaching gen eralization of the Riemann Theta function in the sense that in several con texts their vanishing characterizes the obstruction to the solvability of an associate linear problem\, deeply related to the notion of Lax pair. Si nce their introduction\, the range of applications of Tau functions associ ated to various integrable systems (like Kadomtsev–Petviashvili\, Korteweg -de Vries and generalizations thereof) has expanded well beyond the origin al purview. Applications have been found in Random Matrix Theory and the a ssociated theory of multi-orthogonal polynomials\, enumerative geometry\, combinatorics\, symplectic geometry\, theory of isomonodromic deformations \, integrable probability.\n\nOne week of the workshop will celebrate the work of John Harnad\, whose inspiring activity in the area of integrable s ystems and applications of the theory of tau functions to several problems has spanned three decades.\n\nOrganizers :\n Pascal Baseilhac (CNRS - Univ ersité de Tours)\n Marco Bertola (Concordia University et SISSA)\n Vincent B ouchard (University of Alberta)\n Nicolas Crampé (CNRS\, Université de Tour s)\n Hendrik De Bie (Universiteit Gent)\n Jan Felipe van Diejen (Universidad de Talca)\n Francisco Alberto Grünbaum (University of California\, Berkele y)\n Véronique Hussin (Université de Montréal)\n Luc Lapointe (Universidad d e Talca)\n Makiko Sasada (The University of Tokyo)\n Satoshi Tsujimoto (Kyot o University)\n Robert A. Weston (Heriot-Watt University)\n Sylvie Corteel ( University of California\, Berkeley)\n Alexi Morin-Duchesne (Ghent Universi ty)\n\nhttp://www.crm.umontreal.ca/2022/Systems22/index_e.php\n DTSTART;VALUE=DATE:20220919 DTEND;VALUE=DATE:20221007 SUMMARY:Integrable systems\, exactly solvable models and algebras URL:https://www.mcgill.ca/mathstat/channels/event/integrable-systems-exactl y-solvable-models-and-algebras-341763 END:VEVENT END:VCALENDAR