Birationality in complex and symplectic geometries

September 25-28, 2023

The objective of this workshop is to compare the new trends in birational equivalence in both Kähler/complex geometry and symplectic geometry/topology. Degeneration techniques and newly discovered invariants are key and currently an exciting aspect in both domains. Another common ground that will be represented is hyperkähler or irreducible holomorphic symplectic varieties, a massive focus currently investigated by many leading experts in complex algebraic geometry. We will also focus on the similarities pertaining to symplectic 4-manifolds and complex algebraic surfaces, with the intention of discovering shared methodologies for classifying objects in both domains. For instance, a comparison can be drawn between the application of Gromov’s theory of pseudoholomorphic curves in the study conducted by Lalonde and McDuff on ruled symplectic 4-manifolds or Biran, Pinsonnault and Anjos in later works, and the utilization of Mori’s theory of extremal rational curves in the birational classification of algebraic varieties.

We aim to contribute and advance our understanding of the higher dimensional birational classification problem with the hope of unblocking some of the longstanding issues within both the complex and symplectic categories.

The workshop will consist of two mini-courses and several research talks. The two mini-courses will be given by Tian-Jun Li and Karol Palka. The first one will focus on symplectic Calabi-Yau surfaces and more general compact symplectic surfaces. The second mini-course will discuss the birational geometry of log surfaces. The additional research talks will present recent forefronts and advances in related topics.

In addition to our invited speakers, we intend to involve researchers, graduate students and postdoctoral fellows. Persons interested in participating in the workshop (either in person or virtually) are encouraged to express interest to any of the organizers directly.