Abstract: In this talk, I will review some classical methods computing stable homotopy groups of spheres at the prime 2, and report some recent progress using motivic homotopy theory.

Motivated by Dan Isaksen’s work, Bogdan Gheorghe, Guozhen Wang and myself show that the category of motivic modules over the cofiber of tau and the derived category of BP_*BP comodules are equivalent as stable infinity categories. As a consequence, there is an isomorphism between the motivic Adams spectral sequence of the cofiber of tau and the algebraic Novikov spectral sequence, so one could prove classical Adams differentials through motivic methods. In joint work with Dan Isaksen and Guozhen Wang, we extend the 2-primary computations of stable stems up to the 90’s. If time permits, I will also talk about connections of this project to the Kervaire invariant problem and the new Doomsday conjecture.

There will also be a pretalk in Hylan 1106A at 2 p.m. and dinner with the speaker after the talk.