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Metric Geometry and Geometric Analysis

The purpose of this MSRI summer school is to introduce graduate students to key mainstream directions in the recent development of geometry, which sprang from Riemannian Geometry in an attempt to use its methods in various contexts of non-smooth geometry. This concerns recent developments in metric generalizations of the theory of nonpositively curved spaces and discretizations of methods in geometry, geometric measure theory and global analysis. The metric geometry perspective gave rise to new results and problems in Riemannian Geometry as well.

All these themes are intertwined and have developed either together or greatly influencing one another. The summer school will introduce some of the latest developments and the remaining open problems in these very modern areas, and will emphasize their synergy.

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Venue: University of Oxford

Point Configurations: Deformations and Rigidity

The study of emergent properties of large systems of points is a topic of central importance in the era of big data and of nanotechnology.  The search for robust principles ensuring rigidity and stability of crystalline regular configurations, as well as the conditions of deformability of such structures, forms a truly interdisciplinary topic of great recent interest in mathematics, physics, and computer science.This research school will present several different modern perspectives on the rigidity and deformability of optimum point configurations.  The three lecture course topics are:

Gero Friesecke: Crystallization in classical particle systems
Douglas Hardin and Edward Saff: Discrete energy on rectifiable sets
Danylo Radchenko: Modular forms, universal optimality and Fourier interpolation

These topics will be complemented by tutorial sessions eminent plenary lecturers, presenting links to other fields and enhancing the interdisciplinarity of the school.

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Venue: University College London

18th School on Interactions between Dynamical Systems and Partial Differential Equations (JISD 2022)

This annual meeting of experts and young researchers in Dynamical Systems and PDEs is designed to encourage and enhance exchange of knowledge and methods.  Its goal is to advance the study of cutting edge problems and foster interaction among the participants.​

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Venue: Centre de Recerca Matemàtica, Barcelona

Methods for Random Matrix Theory and Applications

Random matrix theory (RMT) is a crossroad of modern mathematics. It brings together and provides a platform for fusing the ideas of such diverse areas as the theory of special functions, orthogonal polynomials, complex analysis, operator theory, representation of affine algebras and quantum group, enumerative topology, combinatorics, number theory, exactly solvable quantum models, quantum chaos, and string theory.  Simultaneously, RMT plays an increasingly important role in many applied sciences and technologies.

This research school will consist of three lecture courses covering:

Operator theoretic methods and their applications 
Lecturer: Estelle Basor (AIM)

Integrable systems with random initial data
Lecturer: Tamara Grava (Bristol and SISSA)

Panlevé equations and random matrix theory 
Lecturer: Alexander Its (Indiana)

The lecture courses will be supplemented by tutorial sessions and guest lectures by Haaken Hedenmalm (KTH), Gyorgy Geher (Riverlane) and Clay Lecturer Jon Keating (Oxford).

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Venue: University of Reading

Arizona Winter School 2022

The Arizona Winter School is an intensive five-day-long school in which advanced graduate students work closely with senior faculty and postdoctoral fellows. In contrast to a typical conference at which individual researchers present their work in relative isolation, the AWS features a small number of extended courses on a set of closely related topics. The organizers work hard to ensure significant interaction among all participants. Each speaker is assigned a group of students who work with him or her and a postdoctoral assistant on a research project during the Winter School. These students present the results of their research in a lecture at the end of the meeting. Other students work with a postdoctoral assistant in a problem session related to one or more of the lecture series. Still other students work in study groups, carefully learning the material from one the lecture series together. To facilitate work on the projects, problems, and study groups, speakers, assistants, and students meet in evening working sessions.

The 2022 AWS will be held on the topic of Automorphic Forms Beyond GL2.  Professor Akshay Venkatesh will deliver the Clay Lecture.

Automorphic Forms 1
Automorphic Forms 2

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Venue: Online from the University of Arizona

Mathematical Advances in Geophysical Flows

This research school, part of the Jean-Morlet semester on Nonlinear Partial Differential Equations in Fluid Dynamics, focuses on the mathematical study and analysis of geophysical fluid models. As in the case of the Navier-Stokes equations, many of these models still lack, however, basic understanding concerning global existence and existence of smooth solutions. In ocean and atmospheric dynamics, and also in the theory of boundary layers, one is hence investigating often reduced simplified models, whose derivations are based on formal procedures, some of which are not systematic and calling for rigorous validation at the relevant temporal scales.

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Venue: Centre International de Rencontres Mathématiques