Motives and What Not

Motivic zoom conference series

The second edition of our mini-conference will happen on 20th May in Zoom!
The conference is organized by Denis Nardin and me.

The videos of the past talks can be found at our Youtube channel.

To register, please fill by May 19 the following short Google form

The schedule in Central European Summer Time (aka time in Germany):

11:45-12:00 Conference opening

12:00-13:15 Pavel Sechin

13:15-13:45 coffee break

13:45-15:00 Vladimir Sosnilo

15:00-17:00 siesta

17:00-18:15 Peter Haine

18:15-18:45 coffee break

18:45-20:00 Elden Elmanto

Titles and abstracts

Elden Elmanto (Harvard)On the K-theory of universal homeomorphisms
Abstract: I will motivate the study of universal homeomorphism (uh)-invariant theories from the perspective of Grothendieck and the (mixed characteristic) minimal model program. Then I will explain a pullback square examining the behavior of rational K-theory under uh’s and, time permitting, ongoing work on the Brauer stack. This is report on joint work with Mathew and Witaszek. 
 

Peter Haine (MIT)Stratified étale homotopy theory

Abstract: Étale homotopy theory was invented by Artin and Mazur in the 1960s as a way to associate to a scheme X, a homotopy type with fundamental group the étale fundamental group of X and whose cohomology captures the étale cohomology of X with locally constant constructible coefficients. In this talk we’ll explain how to construct a stratified refinement of the étale homotopy type that classifies constructible étale sheaves of spaces. We’ll also explain how to use condensed mathematics to show that the stratified étale homotopy type also classifies constructible ℓ-adic sheaves. This is joint work with Clark Barwick and Saul Glasman.

 

Pavel Sechin (Duisburg-Essen University)Applications of Landweber-Novikov operations on algebraic cobordism
Abstract: I will try to give an overview of how Landweber-Novikov operations can be used in the study of algebraic cobordism. In particular, these operations allow one to distinguish cobordism-motives of some varieties with isomorphic Chow motives, present obstructions to smoothing of cobordism classes and allow one to compute algebraic cobordism of curves and surfaces. If time permits, applications of symmetric operations of Vishik will be mentioned.

 

Vladimir Sosnilo (Chebyshev Laboratory)Pro-excision for stacks
Abstract: The pro-excision statements for K-theory of rings and schemes play a crucial role in the proof of Weibel's conjecture by Kerz, Strunk, and Tamme. In this talk, we will prove analogous statements for algebraic stacks. This is joint work with Tom Bachmann, Adeel Khan and Charanya Ravi.