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K-theory, algebraic cycles and motivic homotopy theory

Participation in INI programmes is by invitation only. Anyone wishing to apply to participate in the associated workshop(s) should use the relevant workshop application form.

3rd May 2022 to 29th July 2022
Rob de Jeu
Aravind Asok
Charles Doran
Roy Joshua
Marc Levine
James D. Lewis
Ursula Whitcher

Programme Theme

The programme will focus on the areas of Algebraic K-theory, Algebraic Cycles and Motivic Homotopy Theory. These are fields at the heart of studying algebraic varieties from a cohomological point of view, which have applications to several other fields like Arithmetic Geometry, Hodge theory and Mathematical Physics.

It was in the 1960s that Grothendieck first observed that the various cohomology theories for algebraic varieties shared common properties, which led him to explain the underlying kinship of such cohomology theories in terms of a universal motivic cohomology theory of algebraic varieties. The theory of Algebraic Cycles, Higher Algebraic K-theory, and Motivic Homotopy Theory are modern versions of Grothendieck's legacy. In recent years it has seen some spectacular developments, on which we want to build further.

The programme will also specifically explore the connections between the following areas:

  • Algebraic K-theory, Motivic Cohomology, and Motivic Homotopy Theory;
  • Hodge theory, Periods, Regulators, and Arithmetic Geometry;
  • Mathematical Physics.

For this, we shall bring together mathematicians working on different aspects of this broad area for extended periods of time, promoting exchange of ideas and stimulating further progress.

This programme is the continuation of the partly cancelled programme of the same name in 2020. In the 2020 part of the programme a workshop took place, which was aimed at giving a younger generation of mathematicians an overview of and introduction to this interesting, but broad area. During this continuation there will be three conference level workshops, one for each of the three areas listed above, aimed at the latest developments and applications of that area. They will be preceded by several more introductory talks.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons