Topology Seminar
Upcoming Talks
In Autumn 2020, the seminar is joint with Northwestern.
The Uchicago-Northwestern Topology Seminar will meet at 4:00pm on Tuesdays on Zoom unless otherwise noted.
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Prasit Bhattacharya (Notre Dame)
The stable Adams conjecture
The Adams conjecture, perhaps one of the most celebrated results in the subject of stable homotopy theory, was resolved by Quillen and Sullivan independently in the 1970s. Essentially, the Adams conjecture says that the q-th Adams operation on the topological K-theory composed with the J-homomorphism can be deformed continuously to the J-homomorphism itself if localized away from q. The stable enhancement of the Adams conjecture (which is only possible in the complex case) claims that this deformation can be achieved within the space of infinite loop maps from BU to the classifying space of spherical bundles. We recently found that the only accepted proof of the stable Adams conjecture, which is due to Friedlander (1980), has a mistake. In this talk, we will reformulate the statement of the stable Adams conjecture, sketch our new proof of the stable Adams conjecture and discuss some of the ramifications. This is a work joint with N. Kitchloo.
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Akhil Mathew (UChicago)
Descent and vanishing in algebraic K-theory via group actions
I will explain some descent and vanishing results in the algebraic K-theory of ring spectra, motivated by the redshift philosophy of Ausoni-Rognes. These results are all proved by considering group actions on stable ∞-categories and their K-theory, as well as some tools coming from chromatic homotopy theory. Joint work with Dustin Clausen, Niko Naumann, and Justin Noel.
If you have any questions, please contact Danny Xiaolin Shi or Hana Jia Kong.