Equations in Motivic Homotopy
About the project
This project studies motivic homotopy theory, a relatively new subject that allows us to utilize algebraic topology methods to understand the objects of interest in algebraic geometry. The motivic theory has had several spectacular successes in resolving deep mathematical problems. In this project, we develop tools that are well suited for studying not just algebraic varieties but also their symmetries. Spheres are simple yet essential objects of study in geometry, and they are considered in the realm of algebraic geometry. One of the central questions is the classification of all possible mappings of a high-dimensional sphere onto a lower dimension sphere.
The broad fundamental research objectives of the project are:
1) Perform explicit calculations of the universal motivic invariants.
2) Develope the subject of motivic Hochschild homology.
3) Solve structural questions about motivic homotopy theory.
Research council of Norway, Independent projects - project number 312472. Total budget approximately 12,7 mill NOK.
Copenhagen, DMA-Ecole Normale Superieure, Harvard, Milan, Münich, Osnabrück, Reed, Steklov Mathematical Institute, UCLA.
ICM 2022 Satellite "Motives and related topics". 27.6.22-1.7.22, St. Petersberg - Russia