for this workshop
Computations in stable homotopy theory
at the
American Institute of Mathematics, Pasadena, California
organized by
Eva Belmont, Hana Jia Kong, XiaoLin Danny Shi, and Zhouli Xu
This workshop, sponsored by AIM and the NSF, 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
- Filtered/Synthetic spectra techniques in the Last Kervaire Invariant Problem
- Filtered/Synthetic spectra techniques in the computations of equivariant slice spectral sequence
- Computer computations of Adams differentials in the context of classical, motivic, and unstable homotopy groups of spheres
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than May 27, 2025.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email workshops@aimath.org
