Ignacio Barros (Université Paris-Saclay)
Robert Lazarsfeld (Stony Brook University)
Olivier Martin (Stony Brook University)
David Stapleton (University of Michigan)
Susanna Zimmermann (Université d’Angers)
How complicated can an algebraic variety be? From the perspective of birational geometry the simplest varieties are rational or unirational. Determining whether or not a variety is rational is a famously hard problem of classical and modern interest. New techniques developed in the past decade have realized exciting progress in deciding rationality and in understanding the behavior of rationality.
Beyond the rationality problem itself there are many interesting questions one can ask concerning the birational complexity of an algebraic variety. Can one bound its irrationality? What sort of subvarieties cover it? How complicated is its birational automorphism group? What happens over different fields?
Cycle-theoretic techniques, motivic integration, measures of irrationality, degeneration, and derived categorical methods are some of the tools that have been developed to attack these questions in recent years. This workshop will bring together mathematicians involved with these different directions to share ideas and recent progress.This event will be preceded by the RTG/SCGP Graduate Workshop on the Birational Complexity of Algebraic Varieties (December 5-9, 2022, SCGP). We encourage students to attend both events but apply to the graduate workshop only. That application will allow students to express interest in the research workshop as we