Speaker: Eoin Mackall, PhD, University of Maryland, College Park

Title: Chow groups of biquaternion Severi--Brauer threefolds

Abstract: The Chow groups of Severi--Brauer varieties are difficult invariants to compute but, when one can compute them, they give rich information on the structure of associated central simple algebras. In this talk, we'll give motivation for studying Severi--Brauer varieties geometrically by looking for applications to central simple algebras. We then explain the idea behind a new proof of an old result of Karpenko computing the Chow groups of some Severi--Bruaer threefolds which are associated to biquaternion algebras.