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Arizona Winter School 2025

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 2025 AWS will be held on the topic of p-adic groups.  Professor Marie-France Vigneras (Jussieu) will deliver the Clay Lecture.

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Venue: University of Arizona

Rocky Mountain Mathematics Consortium Summer School

This Summer School will bring together leading experts in analysis, partial differential equations, and their applications to summarize recent progress in these topics, exchange ideas towards the solution of open questions, and formulate and develop new problems and avenues of research.

Featuring two introductory mini-courses aimed at graduate students and recent PhDs, and several one-hour invited lectures and short contributed talks given by junior participants, the school aims to introduce prospective and young researchers to a broader mathematical community, facilitating the establishment of professional connections with key figures in their areas of interest.

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Venue: University of Wyoming

AGGITaTE 2024

This school will introduce developments in the theory of moduli spaces to postgraduate research students and early-career researchers. It is organised around three courses, each of which presents a different perspective on the study of moduli spaces, and addresses different problems. The school will give early career researchers the opportunity to learn from the leaders in the field themselves, and to start research in this area. The topics covered in the three planned lecture courses and by the plenary lecturer present research advances achieved in the past 5 years. The school will also provide an exciting opportunity for interaction between different branches of research on moduli theory.

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Venue: University of Essex

Summer School on Galois Representations and Reciprocity

The goal of the summer school is to introduce graduate students, advanced undergraduate students, young researchers, and interested mathematicians in Vietnam, Southeast Asia, and other countries in Asia, to the circle of ideas surrounding the Langlands reciprocity conjecture, including an introduction to automorphy lifting theorems, Galois representations and arithmetic aspects of the theory of modular forms.

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Venue: Vietnam Institute for Advanced Studies in Mathematics

CMI-HIMR Summer School on Symmetry and Randomness

This year’s summer school will focus on the mathematics of symmetry and randomness, where probability theory comes together with analysis, geometry and group theory to help understand highly symmetric structures. 

The mini-courses will present aspects of random walks on infinite graphs and groups in connection with geometric group theory; the mathematics of percolation theory especially on large transitive graphs; as well as spectral and mixing time estimates for finite Markov chains with an emphasis on the cut-off phenomenon, and much more. 

Students will have the opportunity to be introduced to these topics as well as to hear lectures by leading figures in the area.

Short Courses

Tom Hutchcroft (Caltech), Structure vs. expansion: probability on transitive graphs*

Justin Salez (Université Paris-Dauphine), The cutoff phenomenon for finite Markov chains*

Tianyi Zheng (UC San Diego), Random walks on self-similar groups: boundary behaviour and amenability*

*Provisional title

The summer school will also feature guest lectures from Itai Benjamini (Weizmann Institute of Science), Persi Diaconis (Stanford) and Geoffrey Grimmett (Cambridge).

Registration closes on Friday 15 March 2024

This event will be taking place in-person. 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).

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Venue: University of Bristol

V Latin American School of Algebraic Geometry (V ELGA)

The goal of this CIMPA School is to train young mathematicians working in Latin America in some of the most active areas of research in Algebraic Geometry, as well as to promote greater interaction among researchers and students, and to build a network of collaborations.

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Venue: Cabo Frio, Brazil

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.

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Venue: 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.

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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.

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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.

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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.

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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.

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Venue: University of Bristol