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 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.

March 1 – 31, 2019 » New Developments in Free Probability and Applications

Organizers: Benoît Collins (Kyoto), James Mingo (Queen’s), Roland Speicher (Saarland), Dan-Virgil Voiculescu (Berkeley)

The thematic one-month program “New Developments in Free Probability and Applications,” to be held at the CRM in March 2019, will highlight the depth and beauty of Free Probability theory as well as the various connections with other fields.

In the spring of 1991, Dan Voiculescu was the holder of the Aisenstadt chair at the CRM. At this time, free probability was still in its infancy and only known to a small group of enthusiasts. This was going to change. Voiculescu gave the Aisenstadt Lectures on free probability in Montréal, organizing the material and bringing it with the help of his students Ken Dykema and Alexandru Nica into a publishable form. The resulting book was the first volume in the CRM Monograph Series. On the timely occasion of the 50th anniversary of the CRM, our thematic program will take place where the seed was sown, with Dan Voiculescu as one of the scholars-in-residence.

The program activities will be anchored by two one-week workshops. In the other two weeks, we expect to organize a special program aimed at bringing graduate students and postdoctoral fellows quickly to the frontiers of the subject.

The first workshop will be inclined more to the pure side of free probability, in particular: operator algebras and random matrix theory, and the second workshop will put its emphasis on applications, for example quantum information theory and  mathematical physics.

We will focus our attention on recent developments of the field, which include—but are not limited to: traffic freeness, bi-free probability, analysis of free entropy, (free) quantum groups, functional inequalities in free probability, new applications to random matrix theory and quantum information theory, advances in free Malliavin calculus and regularity questions of distributions.