Resolutions in Chromatic Homotopy Theory

Project: Research project

Project Details

Description

This a proposal for research and collaboration in chromatic stable homotopy theory, an area of algebraic topology which uses algebraic and arithmetic geometry to drive calculations and the search for large scale phenomena. The applicant and Hans-Werner Henn (IRMA, Strasbourg) have a long-standing collaboration and the Northwestern-Strasbourg connection, most definitely including various students and postdocs, has resulted in an important strand of work in the field.

Recent developments in this arc of research include the solution of the Chromatic Splitting Conjecture of Hopkins at chromatic height 2, the on-going calculations of Picard Group of the K(n)-local category, and the formulation and partial ratification of a vanishing conjecture for the cohomology of Lubin-Tate Space. This conjecture has proved fundamental, as its solutions unlocks many of the other problems in the area. A very recent development imports the duality theory of compact p-adic analytic groups into chromatic homotopy theory; this has allowed for both new calculations and a conceptual reworking of known results that previously required hard calculation.

While Goerss and Henn have worked together for nearly two decades, most recent work has been with a collaborators such as Agnés Beaudry, who has risen to a leadership role in this area, and other closer-to-tenure mathematicians such as Irina Bobkova and Vesna Stojanoska. There are concert plans to collaborate with both Beaudry and Bobkova in any near-term Simons-funded research.
StatusActive
Effective start/end date9/1/218/31/26

Funding

  • Simons Foundation (712748)

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