Home /  [HYBRID WORKSHOP] Integrable Structures in Random Matrix Theory and Beyond


[HYBRID WORKSHOP] Integrable Structures in Random Matrix Theory and Beyond October 18, 2021 - October 22, 2021
Registration Deadline: November 09, 2021 over 2 years ago
To apply for Funding you must register by: July 18, 2021 about 3 years ago
Parent Program:
Location: SLMath: Eisenbud Auditorium
Organizers LEAD Jinho Baik (University of Michigan), Alexei Borodin (Massachusetts Institute of Technology), Tamara Grava (University of Bristol; International School for Advanced Studies (SISSA/ISAS)), Alexander Its (Indiana University--Purdue University), Sandrine Peche (Université de Paris VII (Denis Diderot))

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Image by Alexei Borodin.
This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register.  This workshop will focus on the integrable aspect of random matrix theory and other related probability models such as random tilings, directed polymers, and interacting particle systems. The emphasis is on communicating diverse algebraic structures in these areas which allow the asymptotic analysis possible. Some of such structures are determinantal point processes, Toeplitz and Hankel determinants, Bethe ansatz, Yang-Baxter equation, Karlin-McGregor formula, Macdonald process, and stochastic six vertex model. Bibliography
Keywords and Mathematics Subject Classification (MSC)
  • Random matrix theory

  • Beta ensembles

  • Log- gases

  • Dyson Brownian motion

  • Non-normal matrices

  • Orthogonal polynomials

  • Hankel determinants

  • Toepliz determinants

  • Riemann-Hilbert problem

  • Biorthogonal ensembles

  • Airy process

  • Sine process

  • Determinantal point processes

  • Kardar-Parisi-Zhang universality

  • Asymmetric simple exclusion process

  • Random growth model

  • Interacting Particle Systems

  • random tilings

  • Gaussian free field

  • Directed polymer

  • Last passage percolation

  • Bethe ansatz

  • Six vertex model

  • Yang-Baxter equation

  • Arctic circle theorem

  • Tracy-Widom distribution

  • Stochastic partial differential equation

  • Stochastic heat equation

  • Stochastic Burgers equation

  • Integrable probability

  • Symmetric polynomials

  • Painleve transcendents

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Oct 18, 2021
08:30 AM - 09:00 AM
  Welcome Tea
09:00 AM - 09:10 AM
09:10 AM - 10:00 AM
  Strong Szego Theorem on a Jordan Curve
Kurt Johansson (Royal Institute of Technology (KTH))
10:20 AM - 11:10 AM
  Large Deviations for Generalized Gibbs Ensembles of the Classical Toda Chain
Alice Guionnet (École Normale Supérieure de Lyon)
11:30 AM - 12:20 PM
  Exact Solution of TASEP and Generalizations
Daniel Remenik (Universidad de Chile)
12:20 PM - 01:30 PM
01:30 PM - 02:20 PM
  Gibbsian Line Ensembles and Beta-Corners Processes
Evgeni Dimitrov (Columbia University)
03:00 PM - 03:30 PM
  Afternoon Tea
Oct 19, 2021
09:10 AM - 10:00 AM
  On Finite-Rank Non-Hermitian Deformations of Random Matrix Ensembles
Yan Fyodorov (King's College London)
10:20 AM - 11:10 AM
  Interacting Diffusions on Positive Definite Matrices
Neil O'Connell (University College Dublin)
11:30 AM - 12:20 PM
  Lecture Hall Tableaux, Non Intersecting Paths and Tilings
Sylvie Corteel (University of California, Berkeley)
12:20 PM - 01:30 PM
01:30 PM - 02:20 PM
  Random Melting Skew Young Diagram
Zhipeng Liu (University of Kansas)
03:00 PM - 03:30 PM
  Afternoon Tea
Oct 20, 2021
09:10 AM - 10:00 AM
  The Two-Periodic Aztec Diamond and Matrix Valued Orthogonality
Arno Kuijlaars (Katholieke Universiteit Leuven)
10:20 AM - 11:10 AM
  Local Universality of the Time-Time Covariance and of the Geodesic Tree for Last Passage Percolation
Patrik Ferrari (Rheinische Friedrich-Wilhelms-Universität Bonn)
11:30 AM - 12:20 PM
  Lozenge Tilings and the Gaussian Free Field on a Cylinder
Marianna Russkikh (Massachusetts Institute of Technology)
12:20 PM - 01:30 PM
03:00 PM - 03:30 PM
  Afternoon Tea
Oct 21, 2021
09:10 AM - 10:00 AM
  Hankel Composition Structures in Random Matrix Theory and Beyond
Thomas Bothner (University of Bristol)
10:20 AM - 11:10 AM
  Properties of the chGUE at the Hard Edge: Spacing Distributions and Universality with External Field
Gernot Akemann (Universität Bielefeld)
11:30 AM - 12:20 PM
  Stationary Half-Space Last Passage Percolation
Alessandra Occelli (Instituto Superior Técnico)
12:20 PM - 01:30 PM
01:30 PM - 02:20 PM
  Fractal Geometry of the KPZ Equation
Promit Ghosal (Brandeis University)
03:00 PM - 03:30 PM
  Afternoon Tea
Oct 22, 2021
09:10 AM - 10:00 AM
  The Riemann Hilbert Problem in Higher Genus and Some Applications
Marco Bertola (Concordia University and SISSA; Concordia University and International School for Advanced Studies (SISSA))
10:20 AM - 11:10 AM
  Marked and Conditional Determinantal Point Processes
Tom Claeys (Université Catholique de Louvain)
11:30 AM - 12:20 PM
  Asymptotic Analysis of the Interaction Between a Soliton and a Regular Gas of Solitons
Ken McLaughlin (Colorado State University)
12:20 PM - 01:30 PM
01:30 PM - 02:20 PM
  The Edge Scaling Limit of the Characteristic Polynomial of the Gaussian β-Ensembles
Gaultier Lambert (Universität Zürich)
03:00 PM - 03:30 PM
  Afternoon Tea