Computations in stable homotopy theory
October 27 to October 31, 2025
at the
American Institute of Mathematics,
Pasadena, California
organized by
Eva Belmont,
Hana Jia Kong,
XiaoLin Danny Shi,
and Zhouli Xu
Original Announcement
This workshop will be devoted to recent advances in computing the stable homotopy groups of spheres. The last 10 years have seen significant progress in this area, driven first by applications of motivic homotopy theory and then more recently by the invention of synthetic/filtered spectra, which generalizes motivic techniques. Last year, Weinan Lin, Guozhen Wang, and Zhouli Xu significantly extended the known range of stable homotopy groups and used these computations to resolve the remaining case of the Kervaire Invariant One problem, which has remained open for about 60 years. This workshop will focus on the advances that made these computations possible, especially those involving machine computations and synthetic techniques, and look for applications of these new techniques, for example to the equivariant slice spectral sequence.
The main topics for the workshop are
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Filtered/Synthetic spectra techniques in the Last Kervaire Invariant Problem
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Filtered/Synthetic spectra techniques in the computations of equivariant slice spectral sequence
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Computer computations of Adams differentials in the context of classical, motivic, and unstable homotopy groups of spheres
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
Workshop videos
