May 14 – June 8, 2018 » Probability in Number Theory

Organizers: Andrew Granville (Montréal), Dimitris Koukoulopoulos (Montréal), Maksym Radziwill (McGill)

The appearance of Probability in Number Theory can be traced back to a famous collaboration of Erdős and Kac. Nowadays, probabilistic techniques are routinely used in the study of integers and L-functions. However, until recently there had not been much room for modern and deep techniques of probability theory. During the past few years this has changed notably. Conversely, number theoretic techniques and heuristics have been proven effective in resolving standing problems in combinatorics and discrete probability theory. The goal of this month-long program is to bring together experts from Number Theory and Probability to highlight and facilitate the interactions between these two fields of mathematics.

During the first week of our program, there will be a workshop aimed at young researchers (postdocs and advanced graduate students) who work or are interested in the field of Probabilistic Number Theory. The workshop will consist of mini-courses given by Kevin Ford (Illinois), Adam Harper (Warwick), K. Soundararajan (Stanford) and Terence Tao (UCLA).

The remainder of the program will gather at CRM several of the leading experts in the fields of Probability and Number Theory. We also invite applications for five month-long postdoctoral positions (details to follow). Among other things, we will run a frequent research seminar for the participants of our program.

July 2 – 6, 2018 » A Celebration of CICMA’s Postdoctoral Program

Organizers: Henri Darmon (McGill), Andrew Granville (Montréal)

The goal of this workshop will be to host the CRM–ISM postdoctoral fellows who have worked in the Centre Interuniversitaire en Calcul Mathématique Algébrique (CICMA) over the last 30 years or so. CICMA includes researchers working in number theory, group theory, and algebraic geometry. The large majority of our postdoctoral fellows have launched successful academic careers of their own, and since then have maintained close ties with CICMA, contributing to its success by sending their students to Montréal and, in some cases, through continued exchanges and collaborations with permanent CICMA members. The CRM 50th anniversary provides an opportunity to bring these researchers back to Montréal and celebrate their achievements and contributions to the scientific life of the number theory group.

July 9 – 20, 2018 » Montréal Summer Workshop on Challenges in Probability and Mathematical Physics

Organizers: Alexander Fribergh (Montréal) , Louigi Addario-Berry (McGill), Omer Angel (British Columbia)

This event is similar to a short thematic semester. There will be a light schedule of talks, leaving a lot of free time to encourage collaborations between participants and promote discussions between members of different subfields in probability theory.

The central topic of the workshop will be random media, with an emphasis on the following themes: spin glasses, percolation problems in two dimensions, branching Brownian motions and log-correlated fields, Liouville quantum gravity, random walks in random environments and random graphs.

Each lecture day will be focused on one particular theme; speakers will be asked to focus their talks on open problems and tools that need to be developed in order to encourage collaborations between participants.

The workshop, a satellite activity of the XIX International Congress on Mathematical Physics that will be held in Montréal on July 23-28,  is jointly supported by the Centre de recherches mathématiques and by the Pacific Institute for the Mathematical Sciences.

September 10 – 28, 2018 » Faces of Integrability

Organizers: Jacques Hurtubise (McGill), Nicolai Reshetikhin (Berkeley), Lauren K. Williams (Berkeley)

The theory of integrable systems, with its origins in symmetries, has intricate ties to a wide variety of areas of mathematics. Sometimes the ties are straightforward, but in many cases, the links are more complicated, and indeed somewhat difficult to make explicit.  Some of these interfaces, between integrability, geometry, representation theory, and probability theory will be dominating subjects during the conference and satellite activities.  Themes to be covered include the role of cluster algebras and cluster varieties in the description of moduli spaces, the links between integrable systems and representation theory appearing in such areas as quantum groups and quantization of moduli spaces, and the fascinating interfaces of probability theory, combinatorics and integrable systems appearing in several processes linked to statistical mechanical models.

During the first week of activities, introductory lectures for graduate students will take place, as well as research seminars and discussions. The conference will take place during the second week. During the third week, research discussions and seminars will continue together with follow-up lectures for graduate students.

September 17 – October 14, 2018 » Algebra, Combinatorics, and Mathematical Computer Science

Organizers: François Bergeron (UQAM), Srečko Brlek (UQAM), Christophe Hohlweg (UQAM)

On the occasion of CRM’s 50th anniversary in 2018, the Laboratoire de Combinatoire et d’Informatique Mathématique (LaCIM) organizes a month of scientific activities to discuss the state-of-the-art and manifold interconnections between the lively topics that have long been at the core of research at LaCIM: algebraic combinatorics, combinatorial representation theory, Coxeter groups theory, combinatorics of words, discrete geometry, enumerative combinatorics, mathematical computer science and their applications.  The scientific activities will be articulated around the confirmed participations of two renowned researchers-in-residence:  Mireille Bousquet-Mélou, Directrice de Recherche and Silver Medal of CNRS, and of Ezra Miller, Professor at Duke University; together with a week-long international conference to be held from the 24th to the 28th of September 2018.