# Collection Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

This conference will focus upon three very active fields in algebraic topology and their interactions: chromatic homotopy theory, higher algebraic K-theory, and the development of powerful functorial methods.

Chromatic Homotopy Theory is an important framework which allows the dévissage of the exceedingly complicated stable homotopy category, based upon the geometry of the stack of one-dimensional formal groups, and revealing profound connections with geometry and arithmetic, for example modular forms.

Higher Algebraic K-theory is a fundamental invariant both in arithmetic and geometric topology, taking value in stable homotopy. It remains extremely difficult to compute, but there are important guiding principles involving localizations in chromatic homotopy and Galois descent in the terms of equivariant homotopy theory.

Functorial methods are extremely powerful in modern algebraic topology, a prominent example being Goodwillie calculus, now an essential tool in both homotopy theory and algebra, that has led to computations in algebraic K-theory via topological cyclic homology. The theory also provides powerful tools for the study of stability of homology for families of groups and for performing explicit computations of the cohomology of reductive group schemes.

Recent progress builds upon the far-reaching developments of Higher Algebra and the power of ∞-categories. Interactions with other fields, including (derived) algebraic geometry, number theory, motivic homotopy theory, mathematical physics and category theory lend vitality to the field.

The conference will be the closing event of the ANR project1 ChroK, Chromatic homotopy and K-theory. A major goal is to bring together a wide range of researchers in the above fields, from advanced PhD students to leading experts, to share recent advances in research, discuss the challenges ahead, and to develop collaborations and shape long-term projects.

**Organizer(s)**Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine

**Date(s)**1/23/23 - 1/27/23

**linked URL**https://conferences.cirm-math.fr/2339.html