May 14 – June 1, 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.

The first week of the program (May 14-18) will be dedicated to a summer school featuring lecture series by Kevin Ford (Illinois), Adam Harper (Warwick), and K. Soundararajan (Stanford). We seek applications from young researchers to attend the school. Priority will be given to advanced PhD students and early PhD graduates.

Application for participation is now closed.

The remainder of the program will gather at CRM several of the leading experts in the fields of Probability and Number Theory. 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 17 – October 14, 2018 » Algebra and combinatorics at LaCIM, a conference for the 50th anniversary of the CRM

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

Scientific Committee

• François Bergeron (UQAM);
• Valérie Berthé (Université Paris-Diderot);
• Srecko Brlek (UQAM);
• Laurent Habsieger (Université Claude Bernard, Lyon);
• Sylvie Hamel (UdeM)
• Christophe Hohlweg (UQAM);
• Jean-Christophe Novelli (Université Paris-Est);
• Nathan Reading (North Carolina State University);
• Lauren Williams (UC Berkeley).

escription: 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 Mireille Bousquet-Mélou and Ezra Miller; together with a week-long international conference to be held from the 24th to the 28th of September 2018. This conference will be organized as follows:

* two days session dedicated to subjects related to ties between algebra and combinatorics;
* two days session dedicated to subjects related to ties between combinatorics, theoretical computer science, and statistical physics.

The bridge between the two sessions will be a special event on Wednesday 26th, aiming at underlying 30 years of partnership of LaCIM and CRM through 4 conferences given by:

* Mireille Bousquet-Mélou,
* Ezra Miller,

and by LaCIM’s past and current holders of the Canadian Research Chair, “Algebra, Combinatorics and Mathematical Computer Science”

* Christophe Reutenauer and
* Hugh Thomas.

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.