EWM-EMS Summer School: Chromatic Homotopy Theory and Friends (Web)

Chromatic homotopy theory is a cornerstone in modern algebraic topology. It is a conceptual and computational framework for identifying and explaining large scale periodic patterns in stable homotopy groups. Its origins go back to the work of Adams and Quillen in the 1960s. It became established as an essential computational tool with the work of Miller–Ravenel–Wilson in the 1970s, and a theoretical organizational tool with the work of Devinatz–Hopkins–Smith in the 1980s. Since then, various theoretical developments, such as the Goerss–Hopkins–Miller construction of Morava E- theory and topological modular forms, and Lurie’s establishment of spectrally derived algebraic geometry as a practical tool, have turned chromatic homotopy theory into a cornerstone of algebraic topology.

Beyond its original intentions, chromatic homotopy theory has grown into an organizational principle with applications in areas such as algebraic geometry and modular representation theory. In a different direction, there is a direct yet mysterious relationship between stable homotopy theory and number theory through modular and automorphic forms, as exemplified in work of Behrens and collaborators. Furthermore, the connections to algebraic geometry through motivic homotopy theory are one of the most fruitful lines of research.

This summer school is designed to attract and retain women mathematicians in the field of chromatic homotopy theory. It aims to bring together leading researchers, postdocs, and graduate students working in chromatic homotopy theory and adjacent areas and provide them with an entry point to research in chromatic homotopy theory and opportunity to start collaboration.This workshop is also intended to facilitate mentoring relationships which will improve success and retention of women in chromatic homotopy theory and related areas.