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Trends in Differential and Complex Geometry: a celebration of Nigel Hitchin’s 80th birthday

Hitchin 80

The interactions between geometry, topology, representation theory, and mathematical physics have transformed our understanding of geometric structures and their applications in both pure mathematics and theoretical physics. Geometry has long been at the heart of mathematical advances, with differential and complex geometry playing a fundamental role in many breakthroughs. Over the past half-century, ideas from these fields have influenced areas such as mathematical physics, topology, and number theory, while also evolving through interactions with fields like gauge theory and integrability.

This workshop will explore foundational developments and recent progress, focusing on how core geometric structures continue to shape modern mathematical research. Hitchin’s profound contributions — ranging from Higgs bundles and hyperkähler geometry to generalised complex geometry — have transformed the way we understand and apply geometric structures in modern mathematics. His influence can be seen across multiple areas, providing a central theme that will unify the discussions at this conference.

Speakers: Tom Bridgeland (Sheffield), Robert Bryant (Duke), Simon Donaldson (Imperial), Camilla Felisetti (Modena e Reggio Emilia), Ana Ferreira (Minho), Laura Fredrickson (Oregon), Oscar Garcia-Prada (ICMAT), Michael Groechenig (Toronto), Marco Gualtieri (Toronto), Victoria Hoskins (Essen Duisburg), Jacques Hurtubise (McGill), Ailsa Keating (Cambridge), Marina Logares (Complutense Madrid), Marta Mazzacco (ICREA and UP Catalunya), Ngô Bao Châu (Chicago), Simon Salamon (KCL), José Seade (UNAM), Jörg Teschner (DESY), Richard Thomas (Imperial), Anna Wienhard (MPIM)

Registration: Registration is free but required. To register, please email Naomi Kraker, providing the name of your institution.

Accommodation: A block of accommodation rooms has been reserved at Jesus College for workshop participants. These may be booked and paid for directly by following the link to Jesus College. Scroll to the bottom and click “Book Your B&B Stay Here”, enter the promotion code KX71472 and select your arrival and departure dates. Full details can be found in the Dowloads section below.

Celebratory dinner: Participants will be able to purchase tickets for the celebratory dinner, to be held Wednesday, 2 September at New College. A link for purchasing tickets will be provided when registration has been confirmed.

Financial Aid

Financial support for conference attendees: LMS and Heilbronn

The London Mathematical Society and the Heilbronn Institute for Mathematical Research have both generously given grants to the conference to support the attendance of PhD students and early career researchers who would not otherwise be able to come. Preference (for LMS and HIMR funding only) will be given to the following groups: PhD students at UK universities; participants who are women, or from other groups traditionally under
represented in mathematics; people with caring responsibilities. Following the LMS sustainable events policy, we also have a preference for attendees whose travel will have a low environmental cost (in particular, avoiding long-haul jet travel), and attendees coming from Scotland or mainland Europe are encouraged to consider travelling by train, even if this would be more expensive than flying.
 
For participants supported by these grants, the conference would expect to provide single accommodation for the 5 nights 30 August – Friday 4 September in the block of rooms the conference has reserved at Jesus College, plus a named contribution towards travel costs, which would be paid to the participant after the conference, upon presentation by e-mail or at the conference of travel receipts totalling at least the offered contribution.  

To apply for support to attend the conference, participants should e-mail Naomi Kraker at  admin@claymath.org by 1 June 2026, including the following information:

  • A brief CV, including name, career stage (PhD student, postdoc, etc) and research interestes
  • Dates you want to attend the conference
  • Budget for travel requested, and means (plane, rail, etc)
  • Whether you belong to an under-represented group in mathematics
  • The name and email address o f an academic referee (supervisor preferred for PhD student), who you should ask to send a supporting letter to Naomi Kraker at  admin@claymath.org by 1 June 2026.

Financial support for conference attendees: IMSA

If you are a PhD or Post-Doc from the Americas and would like to apply for lodging or travel support, please use the form below:
https://forms.gle/LMsN4wiynZd5Az2A9

If you are a PhD or Post-Doc and would like the Banquet Subsidy, but do not need other types of financial support (irrespective of your origin) please use the form below:
https://forms.gle/LMsN4wiynZd5Az2A9
Banquet subsidy is automatic for anyone receiving any funding support. 

Participants will be informed whether they are being offered support in early June 2026.

This workshop is organised with support from: Heilbronn Institute of Mathematical Research, London Mathematical Society, National Science Foundation, University of Oxford, University of Chicago at Illinois, Engineering and Physical Sciences Research Council

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Venue: University of Oxford

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Jesus College Room Booking Financial Aid

About Entropy in Large Classical Particle Systems

The goal of this workshop is to get an overview on the use of entropy for the study of large systems of (classical) particles.

  • What is the meaning of kinetic entropy for the particle system?
  • How entropy measures the stability of the system?
  • What entropy dissipation tells about the mixing in the system?
  • Is there a link between entropy and chaos in the probabilistic sense?

These questions are to be declined on several types of models: mean field limits for the Kac model or for Vlasov-Poisson type models, kinetic limits, but also if possible the connections with the area of dynamical systems.

The aim is to gather people from different communities: physicists and mathematicians working on different areas, including PDEs, probability, and dynamical systems.

Speakers:  Viviane Baladi (LPSM Paris), Giada Basile (Sapienza), Lorenzo Bertini (Sapienza), Freddy Bouchet (CNRS and ENS Paris), Jérôme Buzzi (Paris Saclay), Jean-René Chazottes (CNRS and Ecole Polytechnique), Isabelle Gallagher (ENS Paris), François Golse (Ecole Polytechnique), Arnaud Guillin (Clermont-Auvergne), Daniel Heydecker (MPIM), François Huveneers (KCL), Milton Jara (IMPA), Daniel Lacker (Columbia), Thomas Leblé (Paris-Cite), Joel Lebowitz (Rutgers), Clément Mouhot (Cambridge), Stefano Olla (Paris Dauphine), Matt Rosenzweig (MIT), Juan Soler (Grenada), Herbert Spohn (TU Munich)

Participation in the workshop 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, email Naomi Kraker. Students please also provide a letter of reference from your supervisor. 

HOTEL SCAM ALERT:  Some speakers may be contacted via email or telephone by Travellerpoint.org or similar.  Please be advised that we use no external organizing service.  All emails regarding the workshop will be sent by CMI or a workshop organizer. 

Details

Venue: Mathematical Institute, University of Oxford

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Schedule Abstracts Slides, Giada Basile Slides, Lorenzo Bertini Slides, Freddy Bouchet Slides, Jérôme Buzzi Slides, Jean-René Chazottes Slides, Isabelle Gallagher Slides, François Golse Slides, Arnaud Guillin Slides, Daniel Heydecker Slides, François Huveneers Slides, Milton Jara Slides, Thomas Leblé Slides, Joel Lebowitz Slides, Clément Mouhot Slides, Stefano Olla Slides, Matt Rosenzweig Slides, Laure Saint Raymond Slides, Juan Soler Slides, Herbert Spohn

New Perspectives in the Analytic Theory of Automorphic Forms

This workshop will bring together experts in the theory of automorphic forms and representations on reductive groups, with the aim of highlighting major recent advances and posing challenges for the future. A special emphasis will be given to analytic techniques in higher rank settings, and to interactions with problems of number theoretic significance. Among the topics to be addressed will be subconvex bounds for high degree L-functions, automorphic approaches to equidistribution problems, multiplicity estimates for non-tempered spectra, the Ichino–Ikeda conjecture, and the development of various trace formulae and their applications. 

Speakers:  Edgar Assing (Bonn), Raphaël Beuzart-Plessis (Aix-Marseille), Farrell Brumley (Paris Nord), Pierre-Henri Chaudouard (Jussieu), Shai Evra (HUJ), Wee Teck Gan (NUS), Mathilde Gerbelli-Gauthier (McGill), Subhajit Jana (QMUL), Amitay Kamber (Cambridge), Erez Lapid (Weizmann), Simon Marshall (Wisconsin), Jasmin Matz (Copenhagen), Werner Müller (Bonn), Paul Nelson (Aarhus), Ian Petrow (UCL), Abhishek Saha (QMUL), Sug Woo Shin (Berkeley), Jesse Thorner (Illinois, Urbana-Champaign)

Participation in the workshop 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.  

HOTEL SCAM ALERT:  Some speakers may be contacted via email or telephone by Travellerpoint.org or similar.  Please be advised that we use no external organizing service.  All emails regarding the workshop will be sent by CMI or a workshop organizer. 

Details

Venue: Mathematical Institute, University of Oxford

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Schedule Abstracts

Symplectic Geometry, Low Dimensional Topology, and Quantum Fields

Speakers:  Mohammed Abouzaid (Columbia), Mina Aganagic (Berkeley), Aleksander Doan (UCL and Cambridge), Kenji Fukaya (Stony Brook), Sergei Gukov (Caltech), Monica Jinwoo Kang (Caltech), Rinat Kashaev (Geneva), Maxim Kontsevich (IHES) tbc, Pietro Longhi (Uppsala), Lenny Ng (Duke), Sunghyuk Park (Harvard), Vivek Shende (Berkeley), Ivan Smith (Cambridge), Yan Soibelman (Kansas) tbc, Thomas Walpuski (HU Berlin), Tian Yang (Texas A&M)

Participation in the workshop 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.  

HOTEL SCAM ALERT:  Some speakers may be contacted via email or telephone by Travellerpoint.org or similar.  Please be advised that we use no external organizing service.  All emails regarding the workshop will be sent by CMI or a workshop organizer. 

Details

Venue: Mathematical Institute, University of Oxford

Downloads

Schedule Abstracts

K-stability and Birational Geometry

This workshop will bring together mathematicians working on geometry of Fano varieties (projective varieties with ample anticanonical divisors) and varieties with similar properties. A special emphasis will be given to the problems related to K-stability of Fano varieties and their moduli. Among the topics to be addressed will be the K-stability of Fano varieties with special properties, the explicit description of the K-moduli spaces of Fano varieties, rationality problems for Fano varieties, and stability of polarized varieties in general.

Speakers:  Hamid Abban (Nottingham), Carolina Araujo (IMPA), Paolo Cascini (Imperial), Ana-Maria Castravet (Paris-Saclay), Giulio Codogni (Roma Tor Vergata), Kristin De Vleming (UMass), Thibaut Delcroix (Montpellier), Ruadhai Dervan (Glasgow), Kento Fujita (Osaka), Lena Ji (Michigan), Anne-Sophie Kaloghiros (Brunel), Eveline Legendre (Lyon 1), Jesus Martinez Garcia (Essex), Takuzo Okada (Saga), Zsolt Patakfalvi (EPFL), Arman Sarikyan (Edinburgh), Cristiano Spotti (Aarhus), Hendrik Suess (Jena), Nivedita Viswanathan (Brunel)

Participation in the workshop 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.  

HOTEL SCAM ALERT:  Some speakers may be contacted via email or telephone by Travellerpoint.org or similar.  Please be advised that we use no external organizing service.  All emails regarding the workshop will be sent by CMI or a workshop organizer. 

Details

Venue: Mathematical Institute, University of Oxford

Downloads

Schedule Abstracts

Gauge Theory and Topology: in Celebration of Peter Kronheimer’s 60th Birthday

Beginning with the work of Donaldson and Floer, the 1980’s saw the development of a powerful circle of ideas relating gauge theory and low-dimensional topology. In the time since, this theory has grown, matured, and developed a wide range of  applications. This workshop celebrates the enduring influence of Peter Kronheimer on this field.

Since the 1980’s the subject has seen many important theoretical developments:  the advent of Seiberg-Witten theory, the construction of Floer homology theories for 3-manifolds, and extensions including the development of equivariant and family invariants. Along the way, it has developed connections with symplectic and contact topology, the theory of sutured manifolds, and Khovanov homology. The theory has had many remarkable geometric applications, including the proof of the Thom Conjecture, the Weinstein Conjecture, the resolution of  thehigh-dimensional Triangulation Conjecture, and new insights into the structure of the concordance and homology cobordism groups.

The workshop will bring experts from around the world together to discuss issues of current interest in the areas of Floer homology, low-dimensional topology, and gauge theory. Topics of particular interest include new developments in gauge theory and geometric PDE’s, including instanton invariants and the family Seiberg-Witten invariant; the topology of 4-manifolds, including advances in topological 4-manifolds and the study of embedded surfaces; and Floer homology for 3-manifolds, including equivariant Floer homology, knot detection and the relations between instanton  and monopole homology.

Speakers:  Mohammed Abouzaid (Columbia), Ali Daemi (Washington, St Louis), Kristen Hendricks (Rutgers), Nigel Hitchin (Oxford), Andras Juhász (Oxford), Hokuto Konno (Tokyo), Maggie Miller (Stanford), Tomasz Mrówka (MIT), Hiraku Nakajima (Kyoto), Peter Ozsváth (Princeton), Lisa Piccirillo (MIT), Arunima Ray (MPIM Bonn), Danny Ruberman (Brandeis), Rosa Sena-Dias (Lisbon), Steven Sivek (MPIM Bonn), Zoltan Szabó (Princeton), Joshua Wang (Harvard), Yi Xie (Peking), Ian Zemke (Princeton), Raphael Zentner (Regensburg)

Registration is now closed.

Details

Venue: Mathematical Institute, University of Oxford

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Schedule Abstracts

RHB70: Analytic Number Theory and Its Interfaces

The subject of analytic number theory, and all of its applications and interactions, has undergone an explosion of activity in the last decade.  Many important classical questions have seen spectacular advances based on new techniques, and methods developed in analytic number theory have had striking impacts in other fields.  

This workshop is organized in honor of Roger Heath-Brown’s 70th birthday, and will bring together leading experts in analytic number theory and its interfaces with additive combinatorics, arithmetic statistics and Diophantine geometry.

Speakers:  Brian Conrey (AIM), Alexandra Florea (Irvine), Kevin Ford (Urbana-Champaign) Andrew Granville (Montreal), Ben Green (Oxford), Henryk Iwaniec (Rutgers), Jon Keating (Oxford), Emmanuel Kowalski (ETH), Kaisa Matomäki (Turku), Sarah Peluse (Princeton), Lillian Pierce (Duke), Maksym Radziwill (Caltech), Per Salberger (Chalmers), Damaris Schindler (Göttingen), K. Soundararajan (Stanford), Trevor Wooley (Purdue)

Registration is closed.

This event is supported by HIMR and UKRI EPSRC.

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Venue: Mathematical Institute, University of Oxford

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Schedule Abstracts

Computational Number Theory, Geometry and Physics (Sage Days 53)

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Venue: Mathematical Institute, University of Oxford

Mathematics of CCC: Mathematical Physics with Positive Lambda

This workshop will bring together experts in the fields of relativity, geometry, partial differential equations, observational cosmology, and particle physics to explore in depth aspects of conformal cyclic cosmology (CCC).

CCC proposes that the Big Bang was not the universe’s origin, but a conformal continuation of an earlier aeon, where aeons occur sequentially, each starting with a big bang and ending with an exponential expansion driven by positive Λ. There is no early inflation, exponential expansion of the previous aeon serving instead. Emissions from previous-aeon black-hole encounters have observational implications, apparently supported in recent analyses of the CMB. Equations governing the transition from aeon to aeon imply creation of a dark material acquiring mass early in the new aeon, related to Higgs-type conformal symmetry-breaking.

This workshop will explore the many mathematical and astrophysical issues raised by CCC, including

  • the extension of Einstein’s equations to the crossover between aeons leading to interesting aspects of PDEs
  • geometrical aspects of conformal geometry
  • galactic dynamics in the very far future
  • the nature of gravitational wave emission from black-hole encounters
  • conventional cosmology
  • energy conservation in general relativity with positive Λ
  • particle physics at very high energy, and also at very low energy, in the presence of positive Λ

Details

Venue: Mathematical Institute, University of Oxford

Mixed Hodge Modules and their Applications

The goal of this workshop is to discuss the basics of mixed Hodge theory, some of its important applications, and recent developments and connections to other areas.

The theory of mixed Hodge modules is a vast generalization of classical Hodge theory. It was introduced by Morihiko Saito in two papers in 1988 and 1990, building on the foundations created by many people during the 1970s and 1980s, such as D-module theory, the theory of perverse sheaves, and the study of variations of mixed Hodge structure and of their degenerations. In spite of its power and of the potential applications to complex algebraic geometry, mixed Hodge modules has remained a largely esoteric field. The main aim of the workshop is to make this theory more accessible.

Introductory lectures will cover the basics of the theory, with particular emphasis on examples and applications. A small number of talks will focus on mixed Hodge modules themselves, explaining the objects and functors, their basic properties, and some of the problems Saito had to overcome when he created the theory. The majority of talks will be dedicated to a specific result in order to show mixed Hodge modules “in action.” The deeper properties of the theory used in each example will be discussed. Additional talks will cover recent developments and connections to other areas, such as generic vanishing theorems, geometric representation theory or Donaldson-Thomas invariants.

CMI Enhancement and Partnership Program

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Venue: Mathematical Institute, University of Oxford

Developing Exceptional Talent in Mathematics

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Venue: Mathematical Institute, University of Oxford

Higher Structures in Topology and Number Theory

Grothendieck-Teichmüller theory goes back to Grothendieck’s celebrated Esquisse d’un programme. In 1991, Drinfeld formally introduced two Grothendieck-Teichmüller groups, the former one related to the absolute Galois group and the latter one related to the deformation theory of a certain algebraic structure (braided quasi-Hopf algebra). Introduced in algebraic topology 40 years ago, the notion of operad has enjoyed a renaissance in the 90’s under the work of Kontsevich in deformation theory. Two proofs of the deformation quantization of Poisson manifolds, one by himself as well as one by Tamarkin, led Kontsevich to conjecture an action of a Grothendieck-Teichmüller group on such deformation quantizations, thereby drawing a precise relationship between the two themes.

More than 10 years after those major results, the underlying theories have now been well understood and we can expect new important discoveries. Recently, some results have been proved at the intersection of Grothendieck-Teichmüller groups, deformation theory, operads and multiple zeta values. These fields of research clearly overlap and lie at the forefront of current research in algebra, algebraic and differential geometry, number theory, topology and mathematical physics. 

The Clay Mathematics Institute will hold a two-day workshop on ‘Higher Structures in Topology and Number Theory’ at the Mathematical Institute of the University of Oxford on 15 and 16 April 2013. The event is a satellite of the ‘Grothendieck-Teichmüller Groups, Deformations and Operads’ programme taking place at the Isaac Newton Institute in Cambridge between January and April 2013. 

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Venue: Mathematical Institute, University of Oxford