Summary

The eCHT Synthetic Spectra Reading Seminar is an online reading seminar in Winter 2022. The target audience is advanced graduate students, postdoctoral researchers, and faculty. More junior graduate students may be accepted if space allows.

Associated to a homology theory we have an Adams spectral sequence, which approximates stable homotopy classes of maps with homological algebra. This intricate and important spectral sequence can be encoded using the homotopy theory of synthetic spectra, which can be thought of as an infinity-categorical deformation interpolating between ordinary stable homotopy and a suitable derived category. This categorical approach, first discovered in the context of motivic homotopy theory, allows for a plethora of new computational techniques and has led to dramatic advances in the knowledge of the stable homotopy groups of spheres.

This reading seminar will focus on infinity-categorical deformations, such as synthetic spectra, the different ways in which they arise, and their relation to spectral sequences.

Participant Expectations

Participants will take turns giving presentations. The seminar organizers will make sure that presenters have written source material upon which to base their presentations. Participants are expected to attend regularly.

Participants are encouraged to skim the source material being presented each week. They are also encouraged to participate in the private share online workspace.

Students are encouraged to obtain independent study credit from their home universities for their participation in the seminar, but this is not required.

Organizers

The seminar is organized by Piotr Pstrągowski (Harvard University) and William Balderrama (University of Virginia). Contact either for more information.

Application

Please submit the application form to apply. Applications received by January 13 will receive full consideration. 

Schedule

The seminar meets regularly at 2:00pm eastern time on Wednesdays, starting January 26 and ending April 27.