# Motivic Hopf equations

## About the project

Frontier research group project funded by the RCN. The principal aim of this funding scheme is to give dynamic research groups the opportunity to develop and become among the internationally leading in their field.

## Principal investigator

Paul Arne Østvær

## Objectives

Our research aims at formulating and solving ground-breaking problems in motivic homotopy theory. As a relatively new field of research this subject has quickly turned into a well-established area of mathematics drawing inspiration from both algebra and topology. By leverage of modern topological methods, this offers powerful ways of studying algebro-geometric objects defined by polynomial equations.

## Financing

Research council of Norway, Independent projects - project number 250399. Total budget approx 20,5 mill NOK.

## Programs

Motivic Geometry; The Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, 2020/2021.

K-Theory, Algebraic Cycles and Motivic Homotopy Theory; Isaac Newton Institute for Mathematical Sciences, 2020.

K-theory and related fields, a Hausdorff trimester program at the Hausdorff research institute for mathematics. 8 May -- 31 August, 2017.

Algebro-geometric and homotopical methods at the Institute Mittag-Leffler. 16 January -- 30 April, 2017.

## Conferences

IHES Summer School, on Motivic, equivariant, and non-commutative homotopy theory. 6-17 July 2020.

Workshop on Algebraic Geometry and Homotopy Theory, October 3-4, 2019 - Radboud University Nijmengen.

School on Motives and Stacks, Essen, September 23 - 27, 2019.

Computations in motivic homotopy theory, hosted by the SFB 1085 Higher Invariants at the University of Regensburg, September 16th-20th, 2019.

Algebraic K-theory at Mathematisches Forschungsinstitut Oberwolfach, 23 June - 29 June 2019

Algebro-Geometric and Homotopical Methods at Institut Mittag-Leffler, 06 May - 10 May 2019

New Trends in K-Theory and Homotopy Theory at Institut Henri Poincare, Paris. A conference in honor of Max Karoubi's 80th birthday. November 15th and 16th 2018.

Homotopy Theory and Arithmetic Geometry: Motivic and Diophantine Aspects at Imperial College London. A summer school of the London Mathematical Society and the Clay Mathematics Institute that is supported by the Heilbronn Institute of Mathematics Research. 9--13 July, 2018

Equivariant homotopy theory and K-Theory at the Freie Universitaet Berlin. 18--22 June, 2018.

Motivic homotopy groups of spheres 3 at the Freie Universitaet Berlin. 25--29 June, 2018.

Motivic homotopy theory and refined enumerative geometry at the Universitaet Duisburg-Essen. 14--18 May, 2018.

Conference on Algebro-Geometric and Homotopical Methods at the Institute Mittag-Leffler. 13--17 March, 2017.

## Seminars of the MHE project

## Guests

Ananyevskiy, Alexey

Ayoub, Joseph

Bachmann, Tom

Baker, Andrew

Banerjee, Anandam

Bergh, Daniel

Bethea, Candace

Binda, Federico

Bruner, Robert

Burghardt, Viktor

Druzhinin, Andrei

Dubouloz, Adrien

Elmanto, Elden

Frankland, Martin

Garkusha, Grigory

Guozhen, Wang

Heller, Jeremiah

Hesselholt, Lars

Horel, Geoffroy

Kahn, Adeel

Kishimoto, Takashi

Kuku, Aderemi

Matthew, Akhil

Nikolaus, Thomas

Pal, Ambrus

Panin, Ivan

Park, Doosung

Quigley, J.D.

Röndigs, Oliver

Spitzweck, Markus

Stojanoska, Vesna

Strunk, Florian

Tanania, Fabio

Vishik, Alexander

Wendt, Matthias

Williams, Ben

Yagunov, Serge

Yakerson, Maria