Grants and Contracts per year
Grants and Contracts Details
Description
The goal of this project is to tackle two open problems in chromatic homotopy theory.
The rst is with regard to the asymptotic behavior of chromatic homotopy theory and the
second is a conjecture of Ravenel's. Intuition towards both of these problems comes from the
study of character theory and power operations and, as part of this project, we will continue
to develop these tools.
With Barthel, we have shown that chromatic homotopy theory is asymptotically alge
braic. The rst goal of this project is to show that chromatic homotopy theory can be
asymptotically approximated by algebra in characteristic p closely connected to the theory
of formal Drinfeld modules. Due to the existence of Drinfeld elliptic modules at all heights,
success in this endeavor should produce interesting higher height variants of topological
modular forms.
Ravenel conjectured that the kernel of the canonical map from the Burnside ring of
a nite group to the K(n)local cohomotopy of the group contains certain virtual Gsets.
With Reeh, we will develop a theory of K(n)local fusion systems. By understanding the
relationship between these combinatorial objects and K(n)local cohomotopy, we hope to
settle Ravenel's conjecture.
Both of these problems interact with a variety of other problems in chromatic homotopy
theory, thus we expect that the tools developed to tackle these problems will be widely
applicable.
1
Status  Finished 

Effective start/end date  10/1/20 → 9/30/22 
Funding
 USIsrael Binational Science Foundation
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Projects
 1 Active

New Tools in Chromatic Homotopy Theory
USIsrael Binational Science Foundation
10/1/19 → 9/30/24
Project: Research project