Topology Seminar

Date: December 8, 2021

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: William Balderrama, University of Virginia

Title: Deformations of homotopy theories and spectral sequences

Abstract: A standard technique in homotopy theory is to compute something homotopical by relating it to something algebraic. A standard example is the Künneth theorem, relating the homology H_*(X x Y) to the Tor groups Tor(H_*X, H_*Y). This reflects a more general homotopical construction, namely the Künneth spectral sequence for computing tensor products of modules over ring spectra. I will describe a novel method of producing ``algebra-to-homotopy'' spectral sequences such as the latter, which proceeds by considering certain deformations of homotopy theories, both stably and unstably.