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Open Problems Seminar |
Seminar SLMath
program Motivic Homotopy Theory: Connections and Applications
Fall 2026
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Schedule: Friday, 11:00 AM–12:00 PM
Location: Eisenbud Auditorium, SLMath
Organizers: F. Déglise, A. Kundu
Overview: This is an open seminar on open problems of any kind related to motivic homotopy theory. Its aim is to stimulate questions and discussions, and also to inform.
Seminar Schedule:
| 09/25 | Frédéric Déglise | Motivic Dimension of Fields |
A theorem of Borel says, in a suitable sense, that the rational K-theory of a number field lives in just one cohomological degree. A classical calculation of Bass and Tate suggests that adjoining a transcendental variable creates exactly one more.
This raises a deceptively simple question: for a finitely generated field, how many motivic cohomological degrees can there be? I will explain how generic motives make the pattern particularly transparent, why the nonzero groups can nevertheless be enormous, and how the resulting open problem is related to the conjectural t-structure on mixed motives. At the end, curves and their Jacobians will suggest a broader version of the question. |
SLMath announcement |
| 10/02 | Andrei Lavrenov | Classification Problems for Quadratic Forms and Progress via Motivic Methods | I will discuss the classification of quadratic forms of given height and degree, a program initiated by Manfred Knebusch, focusing on quadratic forms of height two and on the conjectural classification proposed by Bruno Kahn, as well as several related conjectures and questions. I will survey what is currently known and explain how Vishik used motivic decompositions of projective quadrics to obtain information about the possible dimensions of height two forms. Finally, I will mention some recent joint work related to these questions. | |
| 10/16 | Utsav Choudhury | Comparison of Nori type motivic categories | The talk will present constructions of different Nori type motivic categories, review their known properties, and discuss conjectures and open questions concerning these categories. | SLMath announcement |
| 10/30 | Haoyang Liu | TBA | ||
| 11/06 | TBA | |||
| 11/13 | TBA | |||
| 11/20 | TBA | |||
| 11/27 | TBA | |||
| 12/04 | TBA | |||
| 12/11 | TBA | |||
| 12/18 | TBA | |||
| Date | Speaker | Title | Summary | Notes |