Speaker: Krishna Kumar MV
Affiliation: University of Milan
Title of Talk: Relative A^1-Contractibility and Exotic Motivic Spheres.
Date: May 26, 2026
Time: 11:00:00 Hours
Venue: AG-77

Abstract: The talk sits at the interface of algebraic topology and geometry. The notion of contractibility offers triviality to several invariants while being powerful enough to allow characterization of classical objects such as Euclidean spaces and affine spaces. After introducing the relevant notions from motivic homotopy, we will study the recent advances on the relative A^1-contractibility of smooth schemes, while warning its limitations in higher dimensions. We will then outline to what extent algebraic (motivic) spheres can be characterized up to A^1-homotopy. As an interesting consequence, we will then prove the existence of motivic spheres that are "exotic" using Koras-Russell prototypes, a rich family of smooth affine schemes. Intrigued readers are welcome to have a look at the papers from https://krishmv.github.io/research.html.