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School on Equivariant Methods in Algebraic and Differential Geometry

The programme will start with an introductory school on equivariant methods in algebraic and differential geometry for graduate students, postdocs and those who are interested in learning background material for the programme.

Most participants in the school will be based in Cambridge, but some will be based at the University of Ibadan in Nigeria, where Praise Adeyemo is the local organiser.

Details

Venue: Isaac Newton Institute and University of Ibadan, Nigeria

Arizona Winter School 2024

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 2024 AWS will be held on the topic of Abelian Varieties.  Professor Barry Mazur will deliver the Clay Lecture.

Details

Venue: University of Arizona

IHES Summer School: Recent Advances in Algebraic K-theory

The last few years have witnessed an explosion of progress in algebraic 𝐾-theory. Derived algebraic geometry and non-commutative methods have been refined into powerful tools, especially through the theory of localizing invariants. Trace methods have brought 𝐾-theory and topological cyclic homology closer together than ever before. Perfectoid techniques mean that 𝐾-theory benefits from the recent progress in 𝑝-adic cohomology, such as prismatic cohomology. Condensed mathematics provides at long last a uniform approach to the 𝐾-theory of topological rings. Geometric foundations for motivic stable homotopy theory have been laid and new motivic filtrations have been unearthed.

The goal of the Summer School will be to help bring the participants up to date on these exciting developments, via research lectures, mini-courses, and an Arbeitsgemeinschaft on the topic of syntomic and étale motivic cohomology.

CMI Enhancement and Partnership Program

Details

Venue: IHES

VIASM-ICTP Summer School on Differential Geometry

This school provides an ideal platform for advanced undergraduates, graduate students, and early-career mathematicians to learn the basics of differential geometry in close connection with recent breakthrough developments. Concrete topics include Kähler geometry, Ricci curvature, geometric convergence, and minimal surfaces.

Differential geometry is among the most important fields in mathematics and physics. Indeed, J. Douglas was awarded the first Fields Medal for his remarkable contribution to the study of minimal surfaces in Euclidean space. Around that time, T. Rado, E. Cartan, and others also obtained significant breakthroughs and results that today bear their names. Today the field is as exciting, vibrant, and fruitful as ever. In particular, the recent resolutions of Willmore’s and Lawson’s conjectures bring new insights and resuscitate old techniques, broadening the vision for humankind to enjoy. This summer school would allow experts in the field to gather, share ideas, and pass on their knowledge to the next generations.

CMI Enhancement and Partnership Program

Details

Venue: VIASM, Hanoi

Geometric, Algebraic and Topological Methods in Quantum Field Theory

This is the 11th of a series of summer schools that have taken place in Colombia every other year since July 1999. The topics of these schools lie on the border line between geometry, topology, algebra and quantum field theory, and they offer courses addressed to both physicists and mathematicians with a master’s level in either of the fields. The school consists of five 6hrs mini-courses giving by lecturers who are leader scientists in their respective areas of research, and two courses of prerequisites, one in mathematics and another one in physics.

CMI Enhancement and Partnership Program

Details

Venue: Villa de Leyva, Boyacá, Colombia

CMI-HIMR Summer School on Probabilistic Group Theory

In recent years, probabilistic methods have been at the heart of many spectacular advances in group theory and related areas, finding a diverse range of applications. This summer school will introduce a wide audience of graduate students and early career researchers to some of the most exciting recent developments. The programme will feature four short courses from world-leading experts in the area, together with tutored problem sessions for participants.

Short Courses

Martin Liebeck (Imperial), Generation properties of finite and algebraic simple groups

Cheryl Praeger (Western Australia), Probabilistic group theory from an algorithmic perspective

Aner Shalev (HUJ), Words, groups and probability

Pham Huu Tiep (Rutgers), Character bounds for finite simple groups

The summer school will also feature guest lectures from Emmanuel Breuillard (Oxford), Ben Green (Oxford) and Colva Roney-Dougal (St Andrews).

Accommodation, lunch and subsistence will be provided, while participants are expected to fund their own travel (limited funds may be available for those unable to secure travel costs from their home institution).

Registration

Registration closes on 24th February 2023.

Details

Venue: University of Bristol

19th School on Interactions between Dynamical Systems and Partial Differential Equations (JISD 2023)

The JISD is an annual meeting between experts and young researchers in Dynamical Systems and Partial Differential Equations (PDEs). It is designed to encourage and enhance the exchange of knowledge and methods, with the goal of advancing the study of cutting edge problems in the aforesaid fields of mathematics and with the aim of fostering the interaction among the participants. 

CMI Enhancement and Partnership Program

Details

Venue: Centre de Recerca Matemàtica, Barcelona

Arizona Winter School 2023

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 2023 AWS will be held on the topic of Unlikely Intersections.  Professor Boris Zilber will deliver the Clay Lecture.

CMI Enhancement and Partnership Program

Details

Venue: University of Arizona

NZMRI Summer School: Groups, Geometry and Dynamics

The main focus of the NZMRI’s activities is an annual workshop on a chosen topic of contemporary significance in mathematics. At this workshop some of the world’s best mathematicians give lecture courses and interact with local researchers and graduate students. NZMRI speakers foster student and wider academic engagement with the workshop and other activities around the country.  The 2023 workshop there are seven invited speakers: Ian Agol (Berkeley), Emmanuel Breuillard (Oxford), Martin Bridson (Oxford), Benson Farb (Chicago), Nicolas Monod (EPFL), Anne Thomas (Sydney) and Amie Wilkinson (Chicago). 

CMI Enhancement and Partnership Program

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Venue: Nelson, NZ

Mathematical General Relativity

Mathematical general relativity is the study of mathematical problems related to Einstein’s theory of gravitation. There are interesting connections between the physical theory and problems in differential geometry and partial differential equations. The purpose of this MSRI Summer Graduate School, held in cooperation with INdAM (Istituto Nazionale di Alta Matematica), is to introduce students to some fundamental aspects of mathematical general relativity, with particular emphasis on the geometry of the Einstein constraint equations and the Positive Mass Theorem.  The SGS will reprise the very successful school on Mathematical General Relativity held at MSRI in 2012.

CMI Enhancement and Partnership Program

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Venue: Cortona, Italy

Modern Nonlinear PDE Methods in Fluid Dynamics

This LMS-ERSRC summer school aims to give PhD students and other young researchers the opportunity to attend high quality lectures, delivered by leading international experts, on the analysis of PDE in fluid dynamics. Each of the four main lecture courses will illustrate certain aspects related to the mathematical theory of the incompressible Euler equations. Luigi Ambrosio will present the state-of-the-art on a theory according to which minimizing geodesics on the space of measure-preserving maps on a domain may be regarded as weak solutions of the Euler equations. Camillo De Lellis will describe the ideas around an important recent construction of continuous solutions which dissipate energy for the Euler equations. Adrian Constantin will exhibit the global bifurcation theory approach to existence of large-amplitude free-surface steady water waves with vorticity. Georg Weiss will discuss recent methods and applications in the analysis of regularity and behaviour at singularities in free boundaries.

The titles of the four main lecture courses are:

Variational models for incompressible Euler equations (Luigi Ambrosio, Scuola Normale Superiore, Pisa)
Dissipative solutions of the Euler equations (Camillo De Lellis, University of Zürich)
Bifurcation theory in the context of steady water waves (Adrian Constantin, King’s College, London)
Analysis of singularities in free-boundary problems (Georg Weiss, Heinrich Heine University, Düsseldorf)

CMI Enhancement and Partnership Program

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Venue: University of Reading

CIMPA Research School on Current Trends in Computational Methods for PDEs

The development of computational methods for partial differential equations (PDEs) is a key tool for the development of science and technology. For its development, it is important to have a deep understanding of the classical and new methodologies used in numerical methods. This summer school will provide an overview of some techniques that allow one to address the computational challenges encountered in different applications. Some of these methodologies include : high order approximation, mixed finite elements, discontinuous Galerkin (DG) methods, domain decomposition and multilevel techniques, adaptivity, a-posteriori error analysis, approximation by sampling methods, sparse grids, ENO and WENO schemes and TVD-reconstructions.

CMI Enhancement and Partnership Program

Details

Venue: Indian Institute of Science, Bangalore, India