UAlberta-PIMS Mathematics and Statistics Colloquium: Zinovy Reichstein

I will discuss the following question independently posed by Clark and Saltman around 2007: Given a central simple algebra A over a field K, is there a a genus 1 curve X over K such that A is split by the function field K(X)? Federico Scavia and I recently showed that the answer is "no" in general. I plan to cover some background material on central simple algebras, motivate the question, and explain the strategy of our proof.