Motivic homotopy theory learning seminar 2022

This seminar aims to cover the basic language and results of motivic homotopy theory, and go over applications depending on the interests of the participants. Some topics that may be touched on include Thom spaces, algebraic K-theory, motivic cohomology, and depending on interest, also algebraic cobordism, enumerative geometry, Milnor-Witt groups, the slice filtration, and six functor formalisms

We are only scheduling a few talks in advance while we go over the basics.
Here are some resources: If you would like to participate, contact Roy Magen.
We meet on Fridays 1:30pm-3:00pm in room 307.
Talks
Date Speaker Topic Main resource(s)
September 30 Roy Magen Organizational meeting
October 7 Emily Saunders Quick overview of ∞-categories, commutative monoids, K-theory Section 1 and maybe 2 of Algebraic K-theory from the viewpoint of motivic homotopy theory
October 14 Morena Porzio Basics of the unstable motivic homotopy category Section 2 of Algebraic K-theory from the viewpoint of motivic homotopy theory and
October 21 Andres Fernandez Herrero On the A1-equivalences between Hilb_d(A^infinity), FFlat_d, Vect_{d - 1}, Gr_{d - 1}(A^infinity) Sections 2 and 4 of The Hilbert scheme of infinite affine space and algebraic K-theory
October 28 Andres Fernandez Herrero On the A1-equivalences between Hilb_d(A^infinity), FFlat_d, Vect_{d - 1}, Gr_{d - 1}(A^infinity) Sections 2 and 4 of The Hilbert scheme of infinite affine space and algebraic K-theory
November 4 Patrick Lei On the A1-invertibility after group completion of the map from FFlat to Vect, proof of lemma 4.1 Section 3 and lemma 4.1 of The Hilbert scheme of infinite affine space and algebraic K-theory
November 11 Ben Church Homotopy groups, purity, stability results for Hilbert schemes Section 8 of The Hilbert scheme of infinite affine space and algebraic K-theory
December 2 Roy Magen, Ben Church Stability results for Hilbert schemes, Results on homotopy groups, purity Section 8 of The Hilbert scheme of infinite affine space and algebraic K-theory
December 9 Stable homotopy, motivic spectra
Motivic cohomology
Framed transfers
...