The next Summer School, organized by Zohar Komargodsky (SCGP), Bruno Le Floch (CNRS & LPTHE), Masahito Yamazaki (IPMU), and Elli Pomoni (DESY) will focus on the physical and mathematical underpinnings of anomalies, for two weeks. It will be held at IHES from June 24 to July 5, 2024.

Anton Kapustin (Caltech), Yuji Tachikawa (IPMU), and Xiao-Gang Wen (MIT) are the members of the scientific committee for this 2024 edition.

If you want to participate, please send your application before March 15, 2024. The selected applicants will be informed in mid-April at the latest.

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Symmetries and Anomalies: a Modern Take

Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different anomalies, which may constrain the dynamics or ruin the model’s consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories and string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics, particularly algebraic topology.

This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). 

The courses will be given by:

• Max METLISKI (MIT)
• Clément DELCAMP (IHES)
• Thomas DUMITRESCU (UCLA)
• Shu-Heng SHAO (Stony Brook University)
• Clay CORDOVA (University of Chicago)
• Iñaki GARCÍA ETXEBARRIA (Durham University)
• Yifan WANG (New York U)
• Đàm Thanh Sơn (Univ. of Chicago)

The next Summer School, organized by Benjamin Antieau (Northwestern University), Lars Hesselholt (University of Copenhagen / Nagoya University), and Matthew Morrow (CNRS and Université Paris-Saclay) will focus on the recent advances in algebraic K-theory, for two weeks. It will be held at IHES from July 11 to 29, 2023.

Bhargav Bhatt (IAS and Princeton University / University of Michigan), Wiesia Niziol (CNRS and Sorbonne Université), and Akhil Mathew (University of Chicago) are the members of the scientific committee for this 2023 edition.

In the style of an Oberwolfach Arbeitsgemeinschaft, ten talks will be given during this 2023 Summer School, by postdoctoral participants on the topic of syntomic and étale motivic cohomology.

If you want to participate, please send your application before February 15, 2023. The selected applicants will be informed on mid-April at the latest.

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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 2023 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.

The mini-courses will be given by:

• Johannes Anschutz (University of Bonn)
• Dustin Clausen (University of Copenhagen and IHES)
• Elden Elmanto (Harvard University)
• Ryomei Iwasa (Université Paris-Saclay)
• Georg Tamme (University of Mainz)

The research lectures will be given by:

• Kęstutis ČESNAVIČIUS (CNRS and Université Paris-Saclay)
• Shane KELLY (University of Tokyo)
• Moritz KERZ (University of Regensburg)
• Hana Jia KONG (Institute for Advanced Study)
• Achim KRAUSE (University of Münster)
• Thomas NIKOLAUS (University of Münster)
• Arpon RAKSIT (Massachusetts Institute of Technology)
• Charanya RAVI (Indian Statistical Institute, Bangalore)
• Kirsten WICKELGREN (Duke University)
• Maria YAKERSON (CNRS and Sorbonne Université)

More information on the dedicated webpage.

This is an IHES Summer School organized in partnership with the Clay Mathematical Institute and in part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101001474).

REMINDER: the participants of the Summer School who will come in person have been selected among a lot of applicants. Others, who were not selected but put on a waiting list won’t participate in person because the capacity of the conference center has been reached. Therefore, if you are interested in participating but did not apply or haven’t been selected or invited to come, please register to participate through Zoom and don’t come to IHES. There are no more seats available and those who did apply and were selected through the application process have the priority to participate in person.

Thank you for your understanding and cooperation!

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2022 Summer School on the Langlands program

The next Summer School, organized by Pierre-Henri Chaudouard (IMJ-PRG),  Wee Teck Gan (National Univ. of Singapore), Tasho Kaletha (Univ. of Michigan), and Yiannis Sakellaridis (Johns Hopkins Univ.), will focus on the Langlands program, an area of research still very active, for three weeks. It will be held at IHES from July 11 to 29, 2022.

Gérard Laumon (Univ. Paris-Sud), Colette Mœglin (IMJ-PRG), Bảo Châu NGÔ (Chicago Univ.) and Jean-Loup Waldspurger (IMJ-PRG) are the members of the scientific committee for this 2022 edition.

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45 years of research and more…

It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.

Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality.

Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a geometric space, can be used to organize a lot of developments around reciprocity.

The Summer School will attempt to bring these exciting new directions together and explore their interactions.

Find out more about the invited speakers:
– David BEN-ZVI, UT Austin
– Raphaël BEUZART-PLESSIS, Univ. Aix-Marseille
– Ana CARAIANI, Imperial College
– Jean-François DAT, IMJ-PRG
– Matthew EMERTON, Chicago Univ.
– Laurent FARGUES, IMJ-PRG
– Tony FENG, MIT
– Jessica FINTZEN, Duke Univ. & Cambridge Univ.
– Toby GEE, Imperial College
– Michael HARRIS, Columbia Univ.
– Eugen HELLMANN, Univ. Münster
– Erez LAPID, Weizmann Inst.
– Chao LI, Columbia Univ.
– Lucas MASON-BROWN, University of Oxford
– Sophie MOREL, ENS Lyon
– Bảo Châu NGÔ, Chicago Univ.
– Dipendra PRASAD, IIT Bombay
– Sam RASKIN, Univ. of Texas
– Peter SCHOLZE, Univ. Bonn
– Sug Woo SHIN, UC Berkeley
– Olivier TAÏBI, ENS Lyon
– Akshay VENKATESH, IAS
– Jared WEINSTEIN, Boston Univ.
– Cong XUE, IMJ-PRG
– Zhiwei YUN, MIT
– Wei ZHANG, MIT
– Xinwen ZHU, CALTECH

More information on the dedicated webpage.

The 2021 IHES Summer School on “Enumerative Geometry, Physics and Representation Theory“, held from 5 to 16 July, was organized in a blended version, in which some participants were at IHES in person, and others will participate over Zoom.

This school is open to everybody but intended primarily for young participants, including Ph.D. students and postdoctoral fellows.

The organising committee includes Andrei Negut (Massachussetts Institute of Technology), Francesco Sala (Università di Pisa) and Olivier Schiffmann (CNRS, Faculté des Sciences d’Orsay, Université Paris-Saclay).

Mina Aganagic (University of California at Berkeley), Hiraku Nakajima (Kavli IPMU), Nikita Nekrasov (Simons Center for Geometry and Physics), and Andrei Okounkov (Colombia University) are the members of the scientific committee.

Enumerative Geometry, Physics and Representation Theory

The main theme of this Summer School is enumerative geometry, with particular emphasis on connections with mathematical physics and representation theory. As its core, enumerative geometry is about counting geometric objects. The subject has a history of more than 2 000 years and has enjoyed many wonderful breakthroughs in the golden years of classical algebraic geometry, but we will be interested in more recent developments.

The 2021 Summer School will focus on the following main subjects with mini-courses and advanced talks given by international experts:

• counting curves and sheaves (Gromov-Witten theory, Donaldson-Thomas and related theories);
• gauge theory enumerative geometry (3d gauge theories and Coulomb branches, 4d gauge theories, and Vafa-Witten invariants, etc.);
• applications of enumerative geometry to categorification and low-dimensional topology;
• Hall algebras and their refined versions (cohomological, K-theoric, derived categories).

Mini-courses given by:
Eugene Gorsky (University of California at Davis), Joel Kamnitzer (University of Toronto), Davesh Maulik (Massachusetts Institute of Technology), Rahul Pandharipande (ETH Zürich), Markus Reineke (Ruhr-Universität Bochum), Richard Thomas (Imperial College London).

Advanced Talks given by:
Pierrick Bousseau (CNRS and Université Paris-Saclay), Alexander Braverman (University of Toronto and Perimeter Institute for Theoretical Physics), Tudor Dimofte (University of California at Davis and University of Edinburgh), Lothar Gottsche (ICTP), Michael Groechenig (University of Toronto), Maxim Kontsevich (IHES), Georg Oberdieck (Mathematisches Institut der Universität Bonn), Richard Rimanyi (University of North Carolina at Chapel Hill), Peng Shan (Tsinghua University), Dimitri Zvonkine (Laboratoire Mathématiques de Versailles).

Information on the dedicated web page.

Find all the videos of the summer school :