Mathematics Colloquia and Seminars

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The ellipsoid embedding function generalizes symplectic ball packing problems. For a symplectic manifold, this function determines the minimum scaling factor required for a standard ellipsoid with a given eccentricity to embed symplectically into the manifold. If the function has infinitely many nonsmooth points, it is said to have an infinite staircase. An infinite staircase implies that an infinite number of distinct obstructions are needed to characterize the function. In this talk, we will present partial results addressing the question: when does the ellipsoid embedding function for a convex toric domain have an infinite staircase? This will include joint work with McDuff-Weiler, Pires-Weiler, and upcoming work with Cristofaro-Gardiner and McDuff.