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CRM / Université de Montréal

CRM

Statistique, Théorie des jeux,    Cours et évènements pour étudiants en mathématiques

This workshop will showcase how AI can assist with exploration, computation, and example-generation in number theory. A central goal is to help researchers overcome the initial barriers to using these tools, especially the uncertainty about how to begin. Through presentations in which speakers explain what they have done and how they work, followed by hands-on sessions where participants can experiment directly, the workshop will offer a practical introduction to integrating AI into mathematical research.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Baryonic matter in the Universe is almost exclusively (99,9 \%) in the plasma state, which is one of the four common states (with solid, liquid and gas), having the specificity of being strongly affected by electrical and magnetic fields. Already three generations of plasma physicists have worked at understanding more precisely the dynamics of plasmas, unravelling their secrets and bringing order to what seems by nature chaotic. Still, the plasmas continue to preserve a part of their mystery. First, our project aims to gain more insight into the microscopic reactions induced by the presence of radiation. Secondly, it is to mathematically elucidate how inertial effects coming from the mixing of charged species (like electrons and ions) is able to stabilize the plasma dynamics at very small scales. Incidently, this would bring innovative insight about some specificities of (magnetohydrodynamics).

Mathématiques appliquées (en général),    Physique mathématique

CRM / Université de Montréal

Summer school “Universal Statistics in Number Theory” (May 4 - 15) will introduce the key topics from both sides of the program, including lecture series by probabilists as well as number theorists.

part of Montreal program 2026: Universal Statistics in number theory

Statistique, Théorie des jeux,    Cours et évènements pour étudiants en mathématiques

Recent research shows the ubiquity of random walk models in problems in analytic number theory as well as Gaussian multiplicative chaos and log-correlations. This comes into the distribution of ζ-values on the 1/2-line, sums of multiplicative functions (particularly divisor functions), and even the solution to various Diophantine problems, and shows direct links and inspiration from Quantum chaos theory. Adam Harper will give his three Aisenstadt lectures at the meeting.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The proposed workshop focuses on recent breakthroughs in arithmetic functions, L-functions, and pseudorandomness in Number Theory, as well as new connections to other areas (via both employed methods and applications), such as additive combinatorics, arithmetic statistics, and dynamical systems. Such breakthroughs include the latest advances in the study of various character and exponential sums (e.g., Kloosterman sums), which are powerful and versatile tools for understanding the anatomy of integers; moments, and other averages of L -functions (over number fields and function fields); integers having a prescribed arithmetic structure (e.g., prime, smooth, square-free, sum of two squares), along with their distribution in arithmetic progressions and short intervals, as well as function field analogs of these problems; distribution of elements of multiplicative subgroups; pseudorandomness of arithmetical functions. An essential aspect of these developments is the vast arsenal of tools and techniques that have been conceived, developed, and implemented, ranging from analysis to additive combinatorics, algebraic geometry, and random matrix theory. The proposed workshop will concentrate on the emerging methods that underlie such advances and on possible future directions.

Théorie des graphes et combinatoire,    Statistique, Théorie des jeux