2023 IHES Summer School – Recent Advances in Algebraic K-theory

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).