The next session of the Geometry Seminar of ICMS
will be held on Wednesday, March 20, 2024, at 16:00, in room 403 and via Zoom.
A talk on:
Ellipsoid superpotentials: obstructing symplectic embeddings by singular algebraic curves
will be delivered by Grigory Mikhalkin, University of Geneva.
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.
This time the seminar will not be accessible via Zoom.