Online conference on Statistical Mechanics, Integrable Systems and Probability

April 27 - May 1, everywhere in the world

The entire world has become disconnected. The scientific community has been no exception with cancellations of conferences, seminars, and research visits. We aim to provide an alternative online approach to traditional conferences. The pandemic should not be a barrier for scientists all over the world to connect, present, discuss their results, and collaborate. One can say that personal contact is one of the core features of the conferences, but in current situation we have to adapt and try something new.

The conference we propose is experimental, but successful online approaches can later be incorporated into offline events.

Schedule

All times are US East Coast (see the table below for conversion).

Zoom room: https://virginia.zoom.us/j/92244866948, password: schur

Monday, April 27

8 pm - 9:20 pm • Lauren Williams (Harvard)

The asymmetric simple exclusion process and Macdonald polynomials

The asymmetric simple exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice, initially introduced as a model for translation in protein synthesis. On the other hand, Macdonald polynomials are a remarkable family of multivariate polynomials which generalize Schur polynomials and Hall-Littlewood polynomials. I'll explain how the study of the ASEP on a ring leads to new formulas for Macdonald polynomials (joint work with Corteel and Mandelshtam), as well as a new notion of quasisymmetric Macdonald polynomials (joint with Corteel-Haglund-Mandelshtam-Mason).

Wednesday, April 29

8:30 am - 9:50 am • Alice Guionnet (ENS Lyon)

Large Deviation Principles via Spherical Integrals

Joint work with Serban Belinschi and Jiaoyang Huang. I will discuss how to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical integrals.
10 am - 11:20 am • Dmitry Chelkak (ENS Paris)

Bipartite dimer model: Gaussian Free Field on Lorentz-minimal surfaces

We discuss a new viewpoint on the convergence of fluctuations in the bipartite dimer model considered on big planar graphs. Classically, when these graphs are parts of refining lattices, the boundary profile of the height function and a lattice-dependent entropy functional are responsible for the conformal structure, in which the limiting GFF (and CLE(4)) should be defined. Motivated by a long-term perspective of understanding the `discrete conformal structure’ of random planar maps equipped with the dimer (or the critical Ising) model, we introduce `perfect t-embeddings’ of abstract weighted bipartite graphs and argue that such embeddings reveal the conformal structure in a universal way: as that of a related Lorentz-minimal surface in 2+1 (or 2+2) dimensions. Though the whole concept is very new, concrete deterministic examples (e.g, the Aztec diamond) justify its relevance, and general convergence theorems obtained so far are of their own interest. Still, many open questions remain, the key one being to understand the mechanism behind the appearance of the Lorentz metric in this classical problem, as well as possible links with the Liouville CFT. Based upon recent joint works with Benoît Laslier, Sanjay Ramassamy and Marianna Russkikh.
12 pm - 1:20 pm • Filippo Colomo (INFN, Firenze)

Correlation functions of the domain wall six-vertex model

The six-vertex model is an exactly solvable two-dimensional lattice model of statistical mechanics; in a suitable scaling limit, and under suitable choices of boundary conditions, it develops limit shapes and Arctic curves. In particular, the six-vertex model with domain wall boundary conditions can be regarded as an `interacting' generalization of the famous `free-fermion' problem of domino tilings of the Aztec Diamond. After reviewing the state of the the art in the determination of the limit shape of the model, we shall become more technical, and present recent progresses in the calculation of multiple integral representations for the correlation functions of the mode. Here a crucial role is played by some antisymmetrization identity, generalizing a relation obtained by Tracy and Widom in the context of the asymmetric simple exclusion process. Based on works with L.Cantini, A.Pronko, A.Sportiello.

Friday, May 1

7:30 am - 08:50 am • Ivan Corwin (Columbia)

Asymmetric simple exclusion process: stochastic PDE limits and exact statistics

Like Lauren's talk on Monday, the subject of this talk will be on the asymmetric simple exclusion process (ASEP). I will focus on some (other) remarkable properties of this Markov process, namely the existence of exact formulas for the distribution of its height function, and its limit to the Kardar-Parisi-Zhang stochastic PDE. I will consider these for ASEP on the full line, on the half line, and on a finite interval in contact with particle reservoirs. This talk will touch on joint works with various subsets of my collaborators Guillaume Barraquand, Alexei Borodin, Alisa Knizel, Tomohiro Sasamoto, Hao Shen, Li-Cheng Tsai and Michael Wheeler.
9 am - 10:20 am • Philippe Di Francesco (University of Illinois at Urbana-Champaign and Paris Saclay)

Triangular Ice: from Integrable Combinatorics to Integrable Probability

Alternating Sign Matrices (ASM) are at the confluent of many interesting combinatorial/algebraic problems: Laurent phenomenon for the octahedron equation, configurations of the Square Ice (6 Vertex model), Descending Plane Partitions (DPP), etc. Here we consider the Triangular Lattice version of the Ice model with suitable boundary conditions leading to an integrable 20 Vertex model. Configurations give rise to generalizations of ASM, which we coin Alternating Phase Matrices (APM). We generalize the ASM-DPP correspondence by showing that APM are equinumerous to the quarter-turn symmetric domino tilings of a quasi-Aztec square with a central cross-shaped hole, and obtain a compact determinant formula for their enumeration. We also present combinatorial conjectures for triangular Ice with other types of boundary conditions. Finally, we study the limit shape of large 20 Vertex configurations and obtain an analytic derivation of their arctic phenomenon by use of the Tangent Method of Colomo-Sportiello. This yields in particular the limit shape of large APM, with a piecewise algebraic arctic curve. (joint work with E. Guitter, Institut de Physique Théorique, Université Paris Saclay, France and B. Debin, Université catholique de Louvain, Belgium).

Design of the conference

Talks will be held as meetings in Zoom. Alternatively, speakers can prerecord the talk and it will be streamed live. In both cases, talks will be accompanied by online chat discussion and a Q&A session in Zoom. If the talk uses slides, we will try to make them available online before the beginning of the talk.
“Coffee breaks” and informal discussions (an invaluable part of every conference) will be held in Slack; other announcements will also be posted there.

During informal discussions you are very welcome to present “posters”. Slack will have a separate section for posters and their disscussion. If you want to present your poster please e-mail the PDF to smisp@mtikhonov.com before the conference starts.

Deadline for “poster” submission is April 24

The link to zoom / stream will be published on the website, so anyone can join in. To be added to the Slack coffee break discussions, please register here.

Some basic points to keep in mind:

In zoom, to ask a question please indicate it by a raise of hand (zoom has a built-in option). The host of the event will give you the speaking access.
Feel free to chat in Slack and make private calls during “coffee-breaks” and informal discussions
Please, be patient to possible technical issues that might interfere throught the conference.
All the talks will be recorded and aviable after the live translations, so it’s possible to discuss them afterwards. But please, try to attend the talks online.

Format and timezones

The planned dates are April 27 - May 1, with the following format. There will be three days of plenary talks (April 27, 29 and May 1), at different times to accompant a mixture of timezones. Each day will feature two or three talks.

Date	US East Coast	Paris	Moscow	Japan
Monday, April 27	8PM Monday	2AM Tuesday	3AM Tuesday	9AM Tuesday
Wednesday, April 29	8:30AM Wednesday	2:30PM Wednesday	3:30PM Wednesday	9:30PM Wednesday
Friday, May 1	7:30AM Friday	1:30PM Friday	2:30PM Friday	8:30PM Friday

The rest of the time is devoted so that people can watch recorded talks; have discussions in slack, engage in ad hoc collaboration, and of course so that the participants can attend to other essential business at home.

Organizers

Mikhail Tikhonov (Lomonosov Moscow State University), Leonid Petrov (University of Virginia and ITTP)

If you have any questions you can reach us at smisp@mtikhonov.com