Solvable Lattice Models Seminar

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mathematical physics combinatorics number theory probability quantum algebra representation theory

Stanford University

Audience: Advanced learners
Seminar series time: Thursday 00:00-01:00 in your time zone, UTC
Organizer: Slava Naprienko*
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Solvable lattice models are statistical mechanical systems that can be studied exactly by a method of Baxter, based on the Yang-Baxter equation. This can be understood in terms of quantum groups. Recently particular examples showing symmetry with respect to the Lie quantum super group U_q(\widehat{\mathfrak{gl}}(r|n) arose in two very different contexts: the representation theory of p-adic groups, where such models were used by Brubaker, Buciumas, Bump and Gustafsson to study Iwahori Whittaker functions on metaplectic groups; and in integrable probability, in work recent of Aggarwal, Borodin and Wheeler. We will introduce the topic starting with Baxter's work on six vertex model, then look at more recent work explaining some of the ideas.

The seminar serves both learning and research purposes. We explore applications of solvable lattice models in different areas of mathematics. First we give "learning" talks with history and first results in the area. After that we give several "research" talks on the recent results. Thus, the seminar is friendly for both students and researchers. Feel free to join every new "topic" even if you got lost last time because we start over with introductory talks.

Upcoming talks
Past talks
Your timeSpeakerTitle
WedNov 0223:00Leonid PetrovRewriting History in Integrable Stochastic Particle Systems
WedOct 1923:00Daniel BumpColored Bosonic Lattice Models and Matrix Coefficients
WedOct 1223:00Slava NaprienkoThe free-fermionic Schur functions
TueMay 3121:00William DudarovBi-colored Lattice Models, Charge, and the Combinatorics of Weyl Group Multiple Dirichlet Series
TueApr 0521:00Daniel BumpSupersymmetric Solvable Lattice Models and the Kac module
TueMar 2921:00Amol AggarwalFusion
TueMar 0819:00Christian KorffTBA
TueMar 0122:00Matthew NicolettiIrreversible Markov Dynamics and Hydrodynamics for KPZ Phase in the Stochastic Six Vertex Model
TueFeb 2222:00David Keating$k$-tilings of the Aztec diamond
TueFeb 0822:00Slava NaprienkoIntegrability of the Six-Vertex Model: Generalized Izergin-Korepin Determinant and the deformed Weyl denominator
WedDec 0101:00Claire FrechetteA Lattice Model for Supersymmetric LLT Polynomials
WedNov 2401:00Paul Zinn-JustinShuffle algebras, lattice paths and the commuting scheme
WedNov 1701:00Zhongyang LiAsymptotics of random perfect matchings on rail yard graphs
WedNov 1001:00Ajeeth GunnaModified honeycombs and Factorial dual Grothendieck polynomials
WedNov 0317:00Istvan PrauseIntegrability of limit shapes
WedOct 2700:00Richard KenyonThe five-vertex model
WedOct 2000:00Anamaria SavuIntegrable particle systems for surface diffusion arising from structure and representation of Hecke algebras
WedOct 1300:00Arun RamSpecializations of Macdonald Polynomials
WedOct 0600:00Ben BrubakerColor Me Confused: Cataloguing color in applications of solvable lattice models
WedSep 2900:00Leonid PetrovSchur rational functions, vertex models, and random domino tilings
WedAug 2521:00Anna PuskasA correction factor for Kac-Moody groups and t-deformed root multiplicities
WedAug 1821:00Sasha GarbaliShuffle algebra, Macdonald operators and lattice models
WedAug 1121:00Matteo MucciconiBijective proof of Cauchy and Littlewood identities for q-Whittaker polynomials
WedAug 0421:00Tomohiro SasamotoConnecting q-Whittaker and periodic Schur measures
WedJul 2821:00Jeffrey KuanJoint moments of multi--species $q$--Boson
WedJul 2121:00Jan de GierTransition probabilities and asymptotics for integrable two-species stochastic processes
WedJul 1421:00Jules LamersMacdonald polynomials and long-range spin chains
WedJun 2321:00Alisa KnizelStationary measure for the open KPZ equation
WedJun 1621:00Arun RamLevel 0 modules of affine Lie algebras
WedJun 0921:00Andy HardtHamiltonian operators and free fermionic lattice models
WedJun 0221:00Andrew GitlinA vertex model for LLT polynomials
WedMay 2621:00Nikolaos ZygourasWhittaker functions through polymer models and geometric RSK
WedMay 1921:00Daniel BumpVertex Operators and Solvable Lattice Models
WedMay 1221:00Katherine WeberLattice models as Poincaré pairings
WedMay 0521:00Siddhartha SahiQuasi-polynomial representations of double affine Hecke algebras and a generalization of Macdonald polynomials
WedApr 2821:00Travis ScrimshawRefined dual Grothendieck polynomials from 3 perspectives
WedApr 2121:00Donghyun KimTBA
WedApr 1421:00Sergei KorotkikhLocal relations and q-moments of height functions of stochastic vertex models
WedApr 0721:00Jason SaiedAlcove walk formula for SSV polynomials
WedMar 2421:00Valentin BuciumasSolvable lattice models and special functions appearing in algebraic geometry
WedMar 1721:00Kohei MotegiIzergin-Korepin analysis on wavefunctions
WedMar 1022:00Slava NaprienkoHow to Come Up with Solvable Lattice Models?
WedMar 0322:00Alexey BufetovInteracting particle systems and random walks on Hecke algebras
WedFeb 2422:00Chenyang ZhongStochastic symplectic ice: a stochastic vertex model with U-turn boundary
WedFeb 1722:00Henrik GustafssonA vertex model for Iwahori Whittaker functions
WedFeb 1022:00Leonid PetrovVertex Models and Stochastic Particle Systems
WedFeb 0322:00Ben BrubakerSolvability and Special Functions
WedJan 2722:00Amol AggarwalThe Stochastic Six-Vertex Model
WedJan 2022:00Daniel BumpSolvable lattice models and representations of p-adic groups
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