Apply for funding
for this workshop

Higher-dimensional log Calabi-Yau pairs

September 30 to October 4, 2024

at the

American Institute of Mathematics, Pasadena, California

organized by

Yoshinori Gongyo, Mirko Mauri, Joaquin Moraga, and Roberto Svaldi

This workshop, sponsored by AIM and the NSF, will be devoted to the interactions between the geometry of Calabi-Yau and Fano varieties, and especially their open, degenerate, or logarithmic versions.

Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that measure their combinatorial complexity, explore how additional structures (like the existence of a symplectic form) constrain their geometry, and ultimately recognize that only finitely many geometries of the types above can actually occur.

The main topics for the workshop will be:

  • The birational complexity of log Calabi-Yau pairs and its connection to rationality of smooth Fano varieties and cluster geometry.
  • Mukai's conjecture for Fano varieties and its relation to the generalized complexity.
  • Geometry and deformation of symplectic log Calabi–Yau pairs and its relation to compact hyperkähler and character varieties.
  • Boundedness problems for Calabi–Yau varieties and its connection with moduli theory, e.g., for elliptic Calabi–Yau 3-folds.

This event will be run as an AIM-style workshop. 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 May 15, 2024. 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.

For more information email

Plain text announcement or brief announcement.