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for this workshop

Rationality problems in algebraic geometry

July 29 to August 2, 2019

at the

American Institute of Mathematics, San Jose, California

organized by

Alexander Perry, Alena Pirutka, and Stefan Schreieder

This workshop, sponsored by AIM and the NSF, will be devoted to studying rationality problems in algebraic geometry. Recently, there has been enormous progress in this area, beginning with Voisin's groundbreaking degeneration technique, and its extension by Colliot-Thelene and Pirutka, Totaro, and others. Further development of these ideas led to the proof of irrationality of many varieties that were inaccessible by earlier methods. In these arguments, the obstructions to rationality are cohomological in nature. In a different but related direction, over the past years there has been a growing supply of evidence that the derived category can also be used to detect irrationality.

The goal of this workshop is to consolidate and build on these advances, focusing on the following topics.

  1. Understand the allowable singularities in the degeneration technique, and apply it to new classes of varieties.
  2. Compute birational invariants, e.g. unramified cohomology, in new examples, and look for new obstructions to rationality.
  3. Study instances of the conjectural relation between rationality and derived categories, and investigate the connection to cohomological methods (like the degeneration technique).

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than January 29, 2019. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.

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