RGAS Summer School on Perfectoid Techniques
CMI Enhancement and Partnership Program
Photograph: Sergio Reyes
Details
Venue: La Cristalera, UAM
Home — Research School
CMI Enhancement and Partnership Program
Photograph: Sergio Reyes
Venue: La Cristalera, UAM
Home — Research School
One of the most important events in algebraic geometry over the last decades has been the Summer Research Institute (SRI) in algebraic geometry, held every 10 years. These large, three-week-long meetings with wide international participation from all major research directions in algebraic geometry provide an ideal setting to communicate recent progress and take stock of the breakthroughs in algebraic geometry. The participants include a majority of the top experts in algebraic geometry (from all areas and countries) as well as mid-career mathematicians, postdocs, and advanced graduate students. These meetings also provide a perfect opportunity for close research interactions and new connections between different areas as well as the training of the next generation of researchers in algebraic geometry.
CMI Enhancement and Partnership program
Venue: Colorado State University
Home — Research School
Rigidity properties of geometric and dynamical structures under either symmetry or extremality assumptions, e.g., on curvature or entropy, have been of great interest in both geometry and dynamics for some time. The goal typically is to force such structures to be of classical, often algebraic nature. These ideas and results build on the celebrated works of Mostow, Prasad, Margulis and Zimmer. At the heart lies the discovery that the Mostow–Margulis type rigidity results for discrete subgroups of semisimple Lie groups have far-reaching counterparts in geometry and dynamics.
This school will highlight remarkable progress on several important problems broadly centered around the study of discrete subgroups of Lie groups. Activities will be centered around lecture series and problem sessions by established experts known both for their strong contributions to the field and for the high quality of their mathematical exposition.
CMI Enhancement and Partnership program
Venue: IHES
Home — Research School
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.
CMI Enhancement and Partnership Program
Venue: University of Arizona
Home — Research 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.
CMI Enhancement and Partnership Program
Image: Wikimedia Commons
Venue: University of Wyoming
Home — Research School
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.
CMI Enhancement and Partnership Program
Venue: University of Essex
Home — Research School
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.
CMI Enhancement and Partnership Program
Venue: Vietnam Institute for Advanced Studies in Mathematics
Home — Research School
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.
CMI Enhancement and Partnership Program
Venue: Cabo Frio, Brazil
Home — Research School
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.
CMI Enhancement and Partnership Program
Venue: University of Ibadan, Nigeria
Home — Research School
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.
CMI Enhancement and Partnership Program
Venue: University of Arizona
Home — Research School
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
Venue: IHES
Home — Research School
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
Venue: VIASM, Hanoi