Workshop in Equivariant, Chromatic, and Motivic Homotopy Theory

Northwestern University, Evanston IL

Investigators

Abstract

This is a grant for participant support at the "Workshop on Equivariant, Chromatic, and Motivic Homotopy Theory" to be held at Northwestern University from Monday, March 25 to Friday, March 29, 2013. A remarkable number of the main results in homotopy theory of the past few years have been achieved by calculation, following on and benefiting from a period of building and implementing large theory, especially in derived algebraic geometry. The conference organizers hope to emphasize this point, highlighting the recent calculations and explaining what we have learned about basic homotopy theory. The largest success has been the solution of the Kervaire invariant problem and the attendant resurgence in interest in computational techniques in equivariant stable homotopy theory. Complementing this has been more progress in chromatic homotopy theory, both with large spectra, such as ring spectra coming from the theory of topological automorphic forms, and with small spectra, such as the K(2)-local sphere. There have also been new applications of old techniques, as the use of the Goodwillie calculus to study the EHP sequence and the use of Hochschild homology to make difficult calculations in algebraic K-theory. Partly due to the shock provided by the solution of the Kervaire Invariant Problem, a great many young researchers have entered the field of algebraic topology, ranging from beginning graduate students to junior tenure-line faculty. This grant will be used entirely to support the participation of the members of this cohort in the conference. For those with established or emerging research programs the conference will provide a forum to publicize their work; for more junior researchers, the grant will support their attendance and work to integrate them into the wider community. Further information can be found at the Workshop's website http://www.math.northwestern.edu/~pgoerss/newemphasis/