Motives and What Not

Motivic zoom conference series

The fourth edition of our mini-conference will happen on July 29th in Zoom!
The conference is organized by Denis Nardin and me.

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

If you haven't filled a registration form for a previous edition of our conference,

please fill by July 28th this short Google form

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

11:50-12:00 Conference opening

12:00-13:00 Sabrina Pauli

13:00-13:30 coffee break

13:30-14:30 Doosung Park

14:30-16:30 siesta

16:30-17:30 Tariq Syed

17:30-18:00 coffee break

18:00-19:00 Akhil Mathew

Titles and abstracts

Akhil Mathew (Chicago): On K(1)-local TR
Abstract: The K(1)-localization of algebraic K-theory was first studied by Thomason, who showed that it is filtered by étale cohomology under mild hypotheses. Using some recent advances in the theory of topological Hochschild homology and cyclotomic spectra, I will explain some general properties of K(1)-local TR and an analog of Thomason's result in this context.

Doosung Park (Zurich): Triangulated categories of logarithmic motives over a field

Abstract: There are many non A1-invariant cohomology theories like Hodge cohomology theories. To incorporate these in the framework of triangulated categories of motives, we can instead use a compactification of A1 in logarithmic geometry, which we call Cube. One technical problem is that Cube does not admit a multiplication map, so Cube is not an interval object in the sense of Morel and Voevodsky. In particular, the naive Sing functor is not useful. In this talk, I will explain how to construct a Sing functor for Cube that can be used to compare Voevodsky's motives and logarithmic motives.

Sabrina Pauli (Oslo): Quadratic dynamic and excess intersection
Abstract: One can view Fulton and MacPherson's intersection product of an excess intersection as a limit of proper intersections. In my talk I will introduce a quadratic version of this dynamic process to compute excess intersections in oriented Chow. As an application, I will compute several Euler numbers valued in GW(k), for example the count of lines on a quintic threefold expressed as the sum of local contributions of the lines on the Fermat quintic threefold that deform with a generic deformation.

Tariq Syed (Essen): The cancellation of projective modules of rank 2 with a trivial determinant
Abstract: I will begin with a brief survey of the results on the cancellation problem of projective modules over commutative rings (i.e. algebraic vector bundles on affine schemes). Motivated by this, I will introduce the generalized Vaserstein symbol and explain its applications to the cancellation problem and the generalized Serre question on algebraic vector bundles.