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Equations in Motivic Homotopy

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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-dimensional sphere.

Objectives 

The broad fundamental research objectives of the project are:

1) Perform explicit calculations of the universal motivic invariants.

2) Develop 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, Essen, Harvard, Milan, Münich, Osnabrück, Reed, Steklov Mathematical Institute, Strasbourg, UCLA.

Principal investigator

Paul Arne Østvær

Conferences

Motivic homotopy in interaction, 4.11.24-8.11.24, CIRM, France

Motives in Mainz, 18.3.24 - 22.3.24, Mainz, Germany

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

Kung, Felix
Park, Doosung
Röndigs, Oliver
Druzhinin, Andrei
Yakerson, Mura
Sosnilo, Vova

 

Published Mar. 15, 2021 10:31 PM - Last modified Nov. 9, 2023 11:27 AM

Participants

Detailed list of participants