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From Representation Theory to Mathematical Physics and Back

The theme of the meeting is the continued influence of mathematics and physics on each other. In particular, the workshop will highlight progress in the areas of vertex operator algebras, conformal field theory, representation theory of affine Lie algebras, loop groups, and quantum groups.

Advances in positive representations of real quantum groups and their connections to cluster algebras will be reported on. Recent developments in quantum invariants of 3 and 4-dimensional manifolds coming from mathematical physics and their connections to vertex algebras will also be highlighted. Categorified quantum groups and link invariants from various representation theoretic, algebraic-geometric, and physical perspectives will also be a focus of the workshop.

CMI Enhancement and Partnership Program

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Venue: Stony Brook University

On the Crossroads of Algebra, Geometry and Physics

The goal of this conference is to catalyze new interactions between experts in several interrelated fields, organized broadly around the themes of algebra, geometry and high energy physics.  It will also be an opportunity for broader communities of researchers to learn about the exciting recent developments which have created new and unexpected connections between these diverse subjects.

CMI Enhancement and Partnership Program

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Venue: Yale University

Leuca2022

This conference will gather together experts in the subjects of Diophantine approximation, Diophantine equations, transcendental number theory and arithmetic geometry together with many young talented researchers working in these fields.  It will provide a unique opportunity to discuss the state of the art in many classical topics in these fields and explore new, fast emerging important topics.

CMI Enhancement and Partnership Program

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Venue: Marina di San Gregorio, Patù, Italy

Nonlinear PDEs in Fluid Dynamics

​The field of nonlinear PDEs in fluid dynamics has seen tremendous scientific activities in the last years, which are due to the facts that the underlying governing equations have a very complex structure and that these equations form a building block for other disciplines in sciences.

The mathematical investigations of these systems often follow their traditional lines. Essential progress on certain problems was, however, often based on techniques which were well-known only in other areas or disciplines. This is where the conference comes into its own: besides the investigation of the most recent results on the underlying equations and phenoma, special emphasis will be put to foster the interaction between more fundamental methods in pure mathematics and  current questions arising in the theory of the Navier-Stokes and the Euler equations, in deterministic and stochastic models of complex fluids and in free boundary value problems. Special sessions will be devoted to the presentations of results of younger participants.

CMI Enhancement and Partnership Program

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Venue: Centre International de Rencontres Mathématiques

Probability, Analysis and Dynamics

PAD22 will highlight the major acheivements and breakthroughs in the cross-sections of probability, analysis, and dynamics.  The conference will bring together world-leading scientists to promote the cross-fertilization of ideas between these fields.

CMI Enhancement and Partnership Program

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Venue: University of Bristol

2022 Clay Research Conference

The 2022 Clay Research Conference will be held on Wednesday, 28 September.  The plenary speakers are:

  • Bhargav Bhatt, University of Michigan
  • Kevin Costello, Perimeter Institute
  • Igor Rodnianski, Princeton University
  • Jacob Tsimerman, University of Toronto

Conference Workshops

Associated workshops will be held during the week of the conference, 26-30 September.  The workshops will pause on Wednesday, 28 September for the conference.

p-adic Hodge Theory and Applications (26-30 September)
Organizers:  Bhargav Bhatt (Michigan), Akhil Mathew (Chicago)

Stability and Instability in General Relativity (26-30 September)
Organizers:  Mihalis Dafermos (Cambridge), Elena Giorgi (Columbia), Igor Rodnianski (Princeton)

O-minimality and Diophantine Geometry (26-30 September)
Organizers:  Gareth Jones (Warwick), Alex Wilkie (Manchester and Oxford)

Physics from the Point of View of Geometry (29-30 September)
Organizer:  Ulrike Tillmann (INI and Oxford), Mike Hopkins (Harvard)

Registration for the Clay Research Conference is free but required.  Participation in the workshops is by invitation, but a limited number of additional places is available.  To register for the Clay Research Conference or to register interest in a workshop, please email Naomi Kraker, providing the name of your institution and stating which workshop you wish to attend. Students please also provide a letter of reference from your supervisor.  

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Venue: University of Oxford