# 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.

## Objectives

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.

## Financing

Research council of Norway, Independent projects - project number 312472. Total budget approximately 12,7 mill NOK.

## Cooperation

Copenhagen, DMA-Ecole Normale Superieure, Harvard, Milan, Münich, Osnabrück, Reed, Steklov Mathematical Institute, Strasbourg, UCLA.

## Principal investigator

## Conferences

Harnessing Motivic Invariants, 27.6.22 - 1.7.22, Essen, Germany

Motivic Geometry Conference, 8.8.22 - 12.8.22, Oslo, Norway

## Seminars of the EMOHO project

## Guests