The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas led to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

This will be a split transatlantic conference taking place at the Fields Institute in Canada and the Max Planck Institute for Mathematics in Germany, with videoconferencing connections in place to help collaboration. Please register with the institute that is closest to your location.

Participants interested in contributing a short talk are encouraged to submit their topics by February 28th, 2022 through the provided link: https://docs.google.com/forms/d/e/1FAIpQLSeUhTW27UNZLe8EGUmh-jtAcz9k_nSCwrQwRcHOvRUSMAn4Zw/viewform

Information from the Max Planck Institute for Mathematics for this event can be found here: https://www.mpim-bonn.mpg.de/node/10868 .

Confirmed Speakers

Europe
Joana Cirici - Universitat de Barcelona
Dustin Clausen - University of Copenhagen
Lars Hesselholt - University of Copenhagen
Oscar Randal-Williams - University of Cambridge
Peter Scholze - Max Planck Institute for Mathematics / University of Bonn
Nathalie Wahl - University of Copenhagen
 

North America
Ben Antieau - Northwestern University
David Ayala - Montana State University
Akhil Mathew - University of Chicago
Kate Ponto - University of Kentucky
Jenny Wilson - University of Michigan
Inna Zakharevich - Cornell University