March 12 – 16, 2018 » Workshop in Geometric Analysis and Nirenberg Lectures by Eugenia Malinnikova

Workshop organizers: Pengfei Guan (McGill), Alina Stancu (Concordia), Jérôme Vétois (McGill)

Geometric analysis has seen several major developments in recent years. Some of the most spectacular breakthroughs were made in the last decade and include Perelman’s work on Hamilton’s Ricci flow and his resolution of the Poincaré conjecture and Thurston’s geometrization conjecture; Brendle’s resolution of the Lawson conjecture; the Differentiable Sphere theorem by Schoen and Brendle; and Marques and Neves’ resolution of the Willmore conjecture. It is an ideal time to bring together mathematicians in this area to learn more about the achievements of others, foster collaboration, and enable new breakthroughs.

The workshop will focus on prominent current areas of geometric analysis including, but not limited to, geometric evolution equations, minimal surfaces, conformal geometry, complex structures and Kähler geometry, and applications to relativity. An important theme in this area has been the development and use of sophisticated techniques from the theory of partial differential equations to study natural equations that arise in geometry.

CRM Nirenberg Lectures organizers: Pengfei Guan (McGill), Dima Jakobson (McGill), Iosif Polterovich (Montréal), Alina Stancu (Concordia)

The CRM Nirenberg Lectures in Geometric Analysis have taken place every year since 2014. The series is named in honour of Louis Nirenberg, one of the most prominent geometric analysts of our time. The 2018 lectures will be delivered by Professor Eugenia Malinnikova from the Norwegian University of Science and Technology in Trondheim. Malinnikova’s contributions include a groundbreaking joint work with A. Logunov on the nodal geometry of Laplace eigenfunctions, that has led to a proof of two major conjectures in the field due to Shing-Tung Yau and Nikolai Nadirashvili. The research achievements of Eugenia Malinnikova have been recognized by the 2017 Clay Research Award and an invitation to speak at the 2018 ICM in Rio de Janeiro.

April 14 – May 11, 2018 » Mathematics of Machine Learning

Organizers: Sebastian Bubeck (Microsoft Research), Luc Devroye (McGill), Gábor Lugosi (Pompeu Fabra)

The thematic activity focuses on mathematical challenges of machine learning. The spectacular success of machine learning in a wide range of applications opens many exciting theoretical challenges in a number of mathematical fields, including probability, statistics, combinatorics, optimization, and geometry. The CRM will bring together researchers of machine learning and mathematics to discuss these problems. The principal topics include combinatorial statistics, online learning, and deep neural networks.

The main activities include a workshop on “Combinatorial Statistics” and another one on “Modern Challenges in Learning Theory,” as well as regular seminars given by the invited researchers and scholars-in-residence.

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.

June 11 – July 6, 2018 » Causal Inference in the Presence of Dependence and Network Structure

Organizers: Erica E.M. Moodie (McGill), David A. Stephens (McGill), Alexandra M. Schmidt (McGill)

The goal of most, if not all, statistical inference is to uncover causal relationships, however it is not generally possible to infer causality from standard statistical procedures. In the last three decades, the field of causal inference research has grown at a rapid pace, and yet much of the literature is devoted to relatively simple settings. In this month-long program, we aim to push the frontiers of causal inference beyond simple settings to accommodate complex data with features such as network or spatial structure. We will hold a series of lectures and workshops that address current and novel aspects of causal inference, which involves the uncovering of relationships between variables in an observationally-derived data collection setting. Throughout this program, we will investigate new and challenging settings that have been studied in the conventional statistical literature, but not viewed through the lens of causal inference. The unifying theme of the program is that of complex dependence, with a particular focus on spatial, network, and graphical structures.

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.