## Topology and Geometric Group Theory Seminar

Symplectic embeddings encode changes of coordinates of physical systems, and their properties embody the dichotomy between symplectic rigidity (the features of symplectic geometry which are similar to complex geometry) and flexibility (the features of symplectic geometry which are governed solely by algebraic invariants). In 2012, McDuff and Schlenk proved that the "ellipsoid embedding function" of the ball -- a graphical illustration of the ways varying ellipsoids symplectically embed into the standard symplectic ball -- exhibits an intricate infinite staircase pattern governed by the Fibonacci numbers. We will discuss the tools used to compute the ellipsoid embedding functions of Hirzebruch surfaces, including embedded contact homology capacities and Diophantine equations, and present many new infinite staircases along the way.

There will be a pre-talk by Nicki Magill at 12:15.