Conference Global Portuguese Mathematicians 

13/07/2017, 15:00 — 16:00 — Amphitheatre Pa1, Mathematics Building
Ana Rita Pires, Fordham University

Symplectic embedding problems and infinite staircases

When doing a sphere packing, what is the biggest proportion of the space that can be filled by spheres? The answer depends on how we can deform those spheres: Euclidian packings are the most rigid, whereas volume preserving packings are the most flexible. Symplectic packings fall in the middle, with a mix of rigid and flexible behavior.

In this talk we will relate this question to the more general problem of symplectically embedding ellipsoids into the smallest possible scaling of a target manifold. We will also see how the answer involves infinite staircases, Fibonacci numbers and other recursive sequences, and counting lattice points on triangles.

See also

ARP_s.pdf