Integrable
Probability Working Group
This
is an informal seminar run by Alexei
Borodin, Jimmy He, and Roger Van Peski
and devoted to recent developments related to the integrable
probability in the wide sense.
Join
our mailing
list for the regular announcements.
Talks in Fall 2022:
 THURSDAY, September 15. 3:00pm in 4153 (note: not building 2!)
Guilherme Silva (ICMCUSP): Differential equations for KPZ fixed points.
Abstract: We discuss how multipoint distributions of the KPZ fixed point with narrow wedge initial condition relate to matrix versions of NLS and mKdV systems, and also with matrix KP equation and KP hierarchy. Our approach is via integrable operators, and covers multipoint distributions for the KPZ fixed point, its periodic counterpart, and unravels common features of both of them in an unified way. As we will discuss, our results also contain previously found connections by Tracy and Widom, Adler and van Moerbeke, and others, in the context of the Airy2 process.
 THURSDAY, September 22. 3:00pm in 4153 (note: not building 2!)
Matteo Mucciconi (Warwick): A bijective approach to solvable KPZ models.
I will provide a detailed proof of the bijection at the core of our new approach to study KPZ models. A fundamental ingredient here is the notion of Kashiwara's crystals and their relation to the RSK correspondence, but also to discrete integrable systems such as the boxball system.
 THURSDAY, September 29. 3:00pm in 4153
Cesar Cuenca (Harvard): Random matrices and random partitions at varying temperatures
Abstract: We discuss the globalscale behavior of random matrix eigenvalues and random partitions which depend on the "inverse temperature" parameter beta. The goal is to convince the audience of the effectiveness of the moment method via Fourierlike transforms in characterizing the Law of Large Numbers and Central Limit Theorems. We focus on the regimes of high and low temperatures, i.e., when the parameter beta converges to zero and to infinity, respectively. This talk is based on joint works with Florent BenaychGeorges  Vadim Gorin, and Maciej Dolega  Alex Moll.
 THURSDAY, October 20. 3:00pm in 4153
Misha Goltsblat (Yale): Variations of Schur functions and classical group characters
 THURSDAY, November 3. 3:00pm in 4153
Ryan Mickler (Singulariti): New results on the structure of Jack LittlewoodRichardson coefficients.
Abstract: In 2013, NazarovSkylanin introduced a quantization of the Lax operator $L$ of the BenjaminOno integrable hierarchy on the torus, a 1+1 dimensional classical integrable system of nonlinear dispersive waves. They showed that a particular matrix element of the powers of $L$ provide an infinite family of commuting quantum Hamiltonians which are diagonalised on Jack symmetric functions. We prove a spectral theorem for $L$, showing that its eigenvectors are polynomials which refine Jack symmetric functions. As a consequence, the products of these eigenfunctions refine the algebra of Jack functions. We study these refined products through the introduction of several of tracelike functionals, which reveal a surprising simplicity to the structure of the algebra. Using this technique, we find explicit closedform relations between Jack LittlewoodRichardson coefficients and prove several new cases of a conjecture of Stanley on the structure of these coefficients. [ In part joint work with Alexander Moll and Per Alexandersson (papers to appear in October) ]
 THURSDAY, November 17. 3:00pm in 4153
Zhengye Zhou (Texas A&M): TBA
Abstract: TBA
Talks in Spring 2022:
 THURSDAY, Feb 24. 4:00pm in 4261 (note: not building 2!)
Tomas Berggren (MIT): Domino tilings of the Aztec diamond with doubly periodic weightings
Abstract: In this talk we will discuss random domino tilings of the Aztec diamond with doubly periodic weights. More precisely, asymptotic results of the $ 2 \times k $periodic Aztec diamond will be discussed, both in the macroscopic and microscopic scale. The starting point of the asymptotic analysis is a double integral formula for the associated correlation kernel, which is expressed in terms of a matrix WienerHopf factorization. We will also see a close connection to an associated Riemann surface, with which we will describe the global picture.
 THURSDAY, March 3. 4:00pm in 4261
Alexei Borodin (MIT): sl(11)vertex models: bosonfermion correspondence and determinantal point processes
 THURSDAY, March 10. 4:00pm in 4261
Sergei Korotkikh (MIT): Spin qWhittaker functions and vertex models
Abstract: I will tell about a new family of symmetric functions I've been working on, called inhomogeneous spin qWhittaker functions. They originate from a certain vertex model equivalent to qHahn TASEP and they generalize qWhittaker symmetric functions (t=0 degeneration of Macdonald functions). I will describe how these functions originated from integrable probability and will explain connections to some other families of symmetric functions, namely, spin HallLittlewood functions and interpolation symmetric functions. Time permitting, I will also cover the connection of the model with the representation theory of quantum affine sl_2.
 THURSDAY, March 17. 4:00pm in 4261
Mustafa Alper Gunes (Oxford): Moments of Characteristic Polynomials of Random Matrices, Painleve Equations and Lfunctions
Abstract: In this talk, we will consider various different types of joint moments of characteristic polynomials of random matrices that are sampled according to the Haar measure on classical compact groups. In each case, we will see how one can obtain the asymptotics of these quantities as the matrix size tends to infinity, and see the implications that these asymptotics have regarding moments of Lfunctions. Finally, we will see that these asymptotics have representations in terms of solutions of certain Painleve equations, giving us conjectures relating Lfunctions and solutions of these Painleve systems. Based on a joint work with Assiotis, Bedert and Soor, and some original results obtained as a part of my undergraduate thesis.
 THURSDAY, March 31. 4:00pm in 4261
Promit Ghosal (MIT): Universality of multiplicative statistics of Hermitian random matrix ensembles
Abstract: Multiplicative statistics of random matrix ensembles and their scaling limits are important ingredients for many findings throughout the last few decades. In this talk, we focus on large matrix limit of multiplicative statistics of eigenvalues of unitarily invariant Hermitian random matrices. We show that for onecut regular potential and a large class of multiplicative functional, the associated statistics converge to an universal limit which is described in terms of integrodifferential Painleve II equation. This talk will be based on a joint work with Guilherme Silva.
 THURSDAY, April 7. 3:00pm in 4261 (NOTE UNUSUAL TIME)
Guillaume Barraquand (ENS): Positive random walks in random environment
Abstract: We will consider random walks in random environment and discuss how their asymptotic behavior differs from that of simple random walks. I will first survey what is known about an exactly solvable model on Z, the Beta RWRE. Then I will show that there exists a variant of the model, where the walks are restricted to positive integers, which remains exactly solvable. The large scale behavior of this model present some similarities with the model on Z, but also some differences due to the presence of a boundary. This is a joint work with Mark Rychnovsky.
 THURSDAY, April 14. 4:00pm in 4261
Jimmy He (MIT): Shift invariance of some half space integrable models
Abstract: I'll discuss work in progress on shift invariance in a half
space setting. The starting point is the colored stochastic six vertex
model in a half space, from which we obtain results on the asymmetric
simple exclusion process, as well as for the beta polymer through a
fusion procedure. An application to the asymptotics of a type B analogue
of the oriented swap process is also given.
 THURSDAY, April 21. 4:00pm in 4261
Marianna Russkikh (MIT): Everything you always wanted to know about tembeddings*
*but were afraid to ask
Abstract: We introduce a concept of ‘tembeddings’ of weighted bipartite planar graphs. We believe that these tembeddings always exist and that they are good candidates to recover the complex structure of big bipartite planar graphs carrying a dimer model. We also develop a relevant theory of discrete holomorphic functions on tembeddings; this theory unifies Kenyon’s holomorphic functions on Tgraphs and sholomorphic functions coming from the Ising model.
 THURSDAY, April 28. 4:00pm in 4261
Terrence George (University of Michigan): Shufflings in the dimer model
Abstract: Dominoshuffling is a technique introduced by Elkies, Kuperberg, Larsen and Propp to enumerate and generate domino tilings of the Aztec diamond graph, and was used to give the first proof of the arctic circle theorem. Domino tilings are dual to the dimer model on the square lattice. There are generalizations of dominoshuffling for any biperiodic dimer model, and they form a group called the cluster modular group. This group was studied by Fock and Marshakov, who gave an explicit conjecture for its isomorphism type. We will discuss these generalized shufflings and describe the cluster modular group for any biperiodic dimer model. (joint work with Giovanni Inchiostro).
 THURSDAY, May 5. 4:00pm in 4261
Alexander Moll (UMass Boston): Exact Results for the Quantum BenjaminOno Equation on the Torus
Abstract: In this talk, we use a fractional Gaussian field on the 1dimensional real torus to quantize BenjaminOno waves and give a dynamical interpretation of a result of Stanley (1989). Precisely, the classical BenjaminOno equation on the torus is a nonlinear and nonlocal model of dispersive waves. Starting from the standard Gaussian in the symplectic space of this equation, we construct the quantum BenjaminOno equation on the torus without any path integrals. Remarkably, a result of Stanley (1989) for Jack polynomials implies an exact description of the spectrum of the quantum Hamiltonian in this model. We prove that if one considers BohrSommerfeld quantization of the classical BenjaminOno multiphase solutions on the torus found by SatsumaIshimori (1979), then the resulting approximation of the quantum spectrum found by Stanley is exact after an explicit renormalization of the coefficient of dispersion predicted by AbanovWiegmann (2005).
 THURSDAY, May 12. 4:00pm in 4261
Mirjana Vuletić (UMass Boston/MIT): Free boundary Schur process
Abstract: In this talk I will present our work on the free boundary Schur process, which is a generalization of the original Schur process of Okounkov and Reshetikhin. This model after some shiftmixing is a Pfaffian process. I will introduce combinatorial random corner growth/LPP models corresponding to the free boundary Schur process and present some asymptotic results. The limiting behavior for these models is given by some new deformations of universal distributions of Schur processes. This is a joint work with D. Betea, J. Bouttier, and P. Nejjar.
Talks in Spring 2019:
 TUESDAY, April 2. 3.00pm in
2255
Ryosuke Sato (Nagoya
University): Asymptotic representation theory of
inductive systems of compact quantum groups
 WEDNESDAY,
April 10. 3.00pm in 2255
Claus
Koestler (University College Cork): Characters
of the infinite symmetric group from the viewpoint of
distributional symmetries
 TUESDAY,
May 14. 3.00pm in 2255
Elia
Bisi (Dublin): Transition between characters of
classical groups, decomposition of GelfandTsetlin patterns, and
last passage percolation
Talks in Fall 2018:
 TUESDAY, Sep 18. 3.00pm in 2255
Cesar Cuenca (MIT): A partial qscheme of symmetric
functions
 TUESDAY, Oct 2. 3.00pm in 2255.
Zhongyang Li (UConn): Limit shape of perfect
matchings on squarehexagon lattices
 THURSDAY, Oct 25. 3.00pm in 2136
Benjamin
Brubaker (Minnesota): Whittaker functions from solvable
lattice models and vertex operators
 THURSDAY, Nov 1. 3.00pm in 2136
Pavel Galashin (MIT): Ising Model and Total Positivity
 Nov 13  Nov 15,
TuesdayThursday: FRG Integrable
probability meeting.
Wednesday
lunch signup form (deadline Nov 9)
Tuesday, Nov 13, 3.00pm in 2255
Jiaoyang Huang (Harvard University): The law of
large numbers and central limit theorem via Jack generating
functions.
Wednesday, Nov 14, 11.00am in 2361
Alisa Knizel (Columbia University): Gap
probability function for discrete loggases
Thursday, Nov 15, 2.00pm in 2361
Promit Ghosal (Columbia University):
Tails of the KPZ equation
 TUESDAY, Nov 27. 3.30pm
in 2255.
Maurice Duits (KTH): Doubly periodic tilings and
matrixvalued orthogonal polynomials.
Talks in Spring 2018:
 TUESDAY, March 6. 3.00pm in 2255.
Peter Nejjar(Vienna): Symmetric Last Passage
Percolation and Schur Processes
 TUESDAY, April 3. 3.00pm in 2255.
Alejandro
Morales (Amherst): Hook formulas for skew shapes:
border strips and product formulas
 THURSDAY,
April 26. 1.00pm in 2139.
Cesar Cuenca (MIT): Quantized VershikKerov Theory
and Quantized Central Measures on Branching Graphs
 THURSDAY, April 26. 3.00pm in 2136. CANCELLED
 TUESDAY, May 1. 1.00pm
in 2139.
Konstantin Matveev (Brandeis): Boundary of the Young
graph with Macdonald multiplicities and Kerov’s conjecture
 THURSDAY, May 3. 1.00pm
in 2139.
Konstantin Matveev (Brandeis): Boundary of the Young
graph with Macdonald multiplicities and Kerov’s conjecture
 TUESDAY, May 8. 1.00pm
in 2139.
Leonid Petrov (Virginia): Cauchy identities,
YangBaxter equation, and their randomization
 THURSDAY, May 10. 1.00pm
in 2139.
Nicolai Reshetikhin (Berkeley): The 6vertex model in
statistical mechanics.
 May 14  May 18: Workshop
IntProb2018, Boston
Talks in Fall 2017:
 TUESDAY, September 19. 3.00pm in 2255.
Alexander
Moll (Bonn): Integrability and Fractional Gaussian Fields
in Geometric Quantization
 THURSDAY, September 21. 3.00pm in 2142.
Marianna
Russkikh (Geneva): Playing dominos in different
domains
 THURSDAY, September 28. 3.00pm in 2142.
Herbert
Spohn (Munich): KPZ growing interfaces: How flat is flat?
 TUESDAY, October 3. 3.00pm in 2255.
Jiaoyang
Huang (Harvard): Discrete beta ensembles:
dynamics and universality.
 TUESDAY, Oct 17. 3.00pm in 2255.
Axel
Saenz (University of Virginia): Transition Probabilities
for ASEP on the Ring
 TUESDAY, October 24. 3.00pm in 2255.
Patrik
Ferrari (Bonn): Limit law of a second class
particle in TASEP with nonrandom initial condition
 THURSDAY, Nov 2. 3.00pm in 2142
Cesar
Cuenca (MIT): Interpolation Macdonald operators at infinity
 THURSDAY, Nov 9. 11.30am in 2361
Jeremy
Quastel (Toronto): From TASEP to KPZ fixed point
IMPORTANT: This is a lunch seminar. You can sign up here
before Nov. 1 to reserve a sandwich. Otherwise, please, bring your
own food
 TUESDAY, Nov 14. 3.00pm in 2255
Andrew
Ahn (MIT): Asymptotics of Periodically Weighted Random
Plane Partitions
 TUESDAY, Dec 5. 3.00pm in 2255
Drazen Petrovic (IUPUI): Pfaffian Sign Theorem for the
Dimer Model on a Triangular Lattice
Talks in Fall 2016:
 THURSDAY, October 13. 3.00pm in 2146
Mark
Adler (Brandeis University): Tilings of nonconvex polygons
and limiting processes.
 TUESDAY, November 1. 3.00pm in 2146
Boris
Hanin (MIT): Jack polynomials and 2D beta ensembles
 THURSDAY, November 10. 3.00pm in 2146
Yuchen
Pei (Harvard): A qRSK and its qpolymer
 TUESDAY, November 15. 3.00pm in 2146
Cesar
Cuenca (MIT): Asymptotics of Macdonald and Jack polynomials
 MONDAY, November 21. 3.00pm in 2361
Jon
Novak (UCSD): Semiclassical Asymptotics of GL_N(ℂ) Tensor
Products via Quantum Random Matrices
 TUESDAY, November 29. 3.00pm in 2146
Lingfu
Zhang (MIT): Interlacing adjacent levels of βJacobi
corners processes
 TUESDAY, December 6. 3.00pm in 2146
Asad
Lodhia (MIT): MarchenkoPastur
Law for Kendall's Tau
Talks in Spring 2016:
 THURSDAY, February 4. 3.00pm in 2136.
Alexei
Borodin (MIT):
Stochastic spin models, Lecture 1.
 THURSDAY, February 11. 3.00pm in 2136.
Alexei
Borodin (MIT):
Stochastic spin models, Lecture 2.
 THURSDAY, February 18.
NO
SEMINAR
 THURSDAY, February 25. 3.00pm in 2136.
Yi Sun
(MIT): Laguerre and
Jacobi analogues of the Warren
process
 THURSDAY, March 3. 3.00pm in 2136.
Alisa
Knizel (MIT): Asymptotics of random domino tilings of
rectangular Aztec diamonds
 THURSDAY, March 10.
NO SEMINAR
 THURSDAY, March 17. 3.00pm in 2136.
Alexei
Borodin (MIT):
Stochastic spin models, Lecture 3.
 TUESDAY, March 22. 3.30pm in 2361
Michael
Wheeler (University of Melbourne): The interplay between
quantum integrability and symmetric functions
 THURSDAY, March 31. 3.00pm in 2136.
Alexei
Borodin (MIT):
Stochastic spin models, Lecture 4.
 THURSDAY, April 7. 3.00pm in 2136.
Vadim
Gorin (MIT):
Discrete loop equations and their use in statistical mechanics.
 THURSDAY, April 14. 3.00pm in 2136.
Amol
Aggarwal (Harvard):
On Spin 1/2 Models with (Half) Stationary Initial Data.
 THURSDAY, April 21. 3.00pm in 2136.
Alex
Moll (MIT):
Limit
Shapes: Correspondence Principle as Large Deviations Principle
 THURSDAY,
April 28. 3.00pm in 2136.
Alisa
Knizel (MIT): Gaussian asymptotics of
qRacah ensemble
 THURSDAY, May 5. 3.00pm in 2136.
Alex
Moll (MIT):
Limit
Shapes: Correspondence Principle as Large Deviations Principle 
Lecture 2
Talks in Fall 2015:

TUESDAY, Sep 15. 3.00pm in E18466B.
Jeffrey Kuan (Columbia): Two time distribution
in Brownian directed percolation

THURSDAY, Sep 17. 3.00pm in E17128.
Organizational
meeting: Please, bring with you the articles
and topics which you are interested in and which you would like to
be discussed during the semester.
 THURSDAY, Sep 24. 3.00pm in E17128.
Asad
Lodhia (MIT):
Coulomb Gasses and Renormalized Energy
 THURSDAY, Oct 1.
NO SEMINAR
due to Charles
River Lectures on Probability and Related Topics
on Friday, Oct 2 at MSR
 THURSDAY, Oct 8. 3.00pm in E17128
Vincent
Genest (MIT):
ASEP with open boundaries and Koornwinder polynomials
 THURSDAY, Oct 15. 3.00pm in E17128
Konstantin
Matveev (Harvard):
Efficient quantum tomography
 TUESDAY, Nov 3, 3.00pm in E18358
Michael
La Croix (MIT): The Singular Values of
the GOE
 TUESDAY, Nov 10, 3.00pm in E18358
Evgeni
Dimitrov (MIT): Asymptotic results for a
HallLittlewood process on plane partitions.
 TUESDAY, Nov 24, 3.00pm in E18358
Guillaume
Barraquand (Columbia): First
particle in exclusion processes and the Pfaffian Schur process.