Dreams and nightmares about intersection theory

Intersection theory studies the Chow ring, an algebraic structure whose elements correspond to subvarieties of a variety X, with the ring product reflecting the intersection of subvarieties in X. Thanks to the foundational work of Fulton and MacPherson, this theory is well-understood when X is smooth. In this talk, I will present a naive attempt to extend the definition of the Chow ring to singular schemes — and explain why it fails.

Toni Annala obtained his PhD from the University of British Columbia in 2022. After postdocs at Aalto University and the Institute for Advanced Study, he's going to spend one year as a L.E. Dickson Instructor at the University of Chicago, and then one year as a Simons postdoctoral fellow at Northwestern University. From his doctoral research, he was awarded the Blair Spearman Doctoral Prize by the Canadian Mathematical Society.