Solvable Lattice Models Seminar

mathematical physics combinatorics number theory probability quantum algebra representation theory

Audience:	Advanced learners
Seminar series time:	Thursday 00:00-01:00 in your time zone, UTC
Organizer:	Slava Naprienko*
	*contact for this listing

Seminar website: naprienko.com/lattice-seminar

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 time			Speaker	Title
Wed	Nov 02	23:00	Leonid Petrov	Rewriting History in Integrable Stochastic Particle Systems
Wed	Oct 19	23:00	Daniel Bump	Colored Bosonic Lattice Models and Matrix Coefficients
Wed	Oct 12	23:00	Slava Naprienko	The free-fermionic Schur functions
Tue	May 31	21:00	William Dudarov	Bi-colored Lattice Models, Charge, and the Combinatorics of Weyl Group Multiple Dirichlet Series
Tue	Apr 05	21:00	Daniel Bump	Supersymmetric Solvable Lattice Models and the Kac module
Tue	Mar 29	21:00	Amol Aggarwal	Fusion
Tue	Mar 08	19:00	Christian Korff	TBA
Tue	Mar 01	22:00	Matthew Nicoletti	Irreversible Markov Dynamics and Hydrodynamics for KPZ Phase in the Stochastic Six Vertex Model
Tue	Feb 22	22:00	David Keating	$k$-tilings of the Aztec diamond
Tue	Feb 08	22:00	Slava Naprienko	Integrability of the Six-Vertex Model: Generalized Izergin-Korepin Determinant and the deformed Weyl denominator
Wed	Dec 01	01:00	Claire Frechette	A Lattice Model for Supersymmetric LLT Polynomials
Wed	Nov 24	01:00	Paul Zinn-Justin	Shuffle algebras, lattice paths and the commuting scheme
Wed	Nov 17	01:00	Zhongyang Li	Asymptotics of random perfect matchings on rail yard graphs
Wed	Nov 10	01:00	Ajeeth Gunna	Modified honeycombs and Factorial dual Grothendieck polynomials
Wed	Nov 03	17:00	Istvan Prause	Integrability of limit shapes
Wed	Oct 27	00:00	Richard Kenyon	The five-vertex model
Wed	Oct 20	00:00	Anamaria Savu	Integrable particle systems for surface diffusion arising from structure and representation of Hecke algebras
Wed	Oct 13	00:00	Arun Ram	Specializations of Macdonald Polynomials
Wed	Oct 06	00:00	Ben Brubaker	Color Me Confused: Cataloguing color in applications of solvable lattice models
Wed	Sep 29	00:00	Leonid Petrov	Schur rational functions, vertex models, and random domino tilings
Wed	Aug 25	21:00	Anna Puskas	A correction factor for Kac-Moody groups and t-deformed root multiplicities
Wed	Aug 18	21:00	Sasha Garbali	Shuffle algebra, Macdonald operators and lattice models
Wed	Aug 11	21:00	Matteo Mucciconi	Bijective proof of Cauchy and Littlewood identities for q-Whittaker polynomials
Wed	Aug 04	21:00	Tomohiro Sasamoto	Connecting q-Whittaker and periodic Schur measures
Wed	Jul 28	21:00	Jeffrey Kuan	Joint moments of multi--species $q$--Boson
Wed	Jul 21	21:00	Jan de Gier	Transition probabilities and asymptotics for integrable two-species stochastic processes
Wed	Jul 14	21:00	Jules Lamers	Macdonald polynomials and long-range spin chains
Wed	Jun 23	21:00	Alisa Knizel	Stationary measure for the open KPZ equation
Wed	Jun 16	21:00	Arun Ram	Level 0 modules of affine Lie algebras
Wed	Jun 09	21:00	Andy Hardt	Hamiltonian operators and free fermionic lattice models
Wed	Jun 02	21:00	Andrew Gitlin	A vertex model for LLT polynomials
Wed	May 26	21:00	Nikolaos Zygouras	Whittaker functions through polymer models and geometric RSK
Wed	May 19	21:00	Daniel Bump	Vertex Operators and Solvable Lattice Models
Wed	May 12	21:00	Katherine Weber	Lattice models as Poincaré pairings
Wed	May 05	21:00	Siddhartha Sahi	Quasi-polynomial representations of double affine Hecke algebras and a generalization of Macdonald polynomials
Wed	Apr 28	21:00	Travis Scrimshaw	Refined dual Grothendieck polynomials from 3 perspectives
Wed	Apr 21	21:00	Donghyun Kim	TBA
Wed	Apr 14	21:00	Sergei Korotkikh	Local relations and q-moments of height functions of stochastic vertex models
Wed	Apr 07	21:00	Jason Saied	Alcove walk formula for SSV polynomials
Wed	Mar 24	21:00	Valentin Buciumas	Solvable lattice models and special functions appearing in algebraic geometry
Wed	Mar 17	21:00	Kohei Motegi	Izergin-Korepin analysis on wavefunctions
Wed	Mar 10	22:00	Slava Naprienko	How to Come Up with Solvable Lattice Models?
Wed	Mar 03	22:00	Alexey Bufetov	Interacting particle systems and random walks on Hecke algebras
Wed	Feb 24	22:00	Chenyang Zhong	Stochastic symplectic ice: a stochastic vertex model with U-turn boundary
Wed	Feb 17	22:00	Henrik Gustafsson	A vertex model for Iwahori Whittaker functions
Wed	Feb 10	22:00	Leonid Petrov	Vertex Models and Stochastic Particle Systems
Wed	Feb 03	22:00	Ben Brubaker	Solvability and Special Functions
Wed	Jan 27	22:00	Amol Aggarwal	The Stochastic Six-Vertex Model
Wed	Jan 20	22:00	Daniel Bump	Solvable lattice models and representations of p-adic groups

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