**The International Center for Mathematical Sciences – Sofia (ICMS-Sofia)**

**presents**

## Geometry Seminar of ICMS

20.03.2024, 16:00, Sofia time

ICMS-Sofia, Room 403

**Ellipsoid superpotentials: obstructing symplectic embeddings by singular algebraic curves**

**Ellipsoid superpotentials: obstructing symplectic embeddings by singular algebraic curves**

**Abstract:
**How singular can be a local branch of a plane algebraic curve of a given degree d? A remarkable series of real algebraic curves was constructed by Stepan Orevkov. It is based on even-indexed numbers in the Fibonacci series: a degree 5 curve with a 13/2 cusp, a degree 13 curve with a 34/5-cusp, and so on. We discuss this and other series of algebraic curves in the context of the problem of symplectic packing of an ellipsoid into a ball, with the answer given by the spectacular Fibonacci staircase of McDuff and Schlenk. The aspect ratio a>1 of the ellipsoid can be viewed as a real parameter for a certain enumerative superpotential function, which is mostly locally constant, but jumps at certain specific rational values (responsible for the aspects of cusp singularities). Based on joint work with Kyler Siegel.