Note Friday date. Joint with Cornell Topology Festival.

One of the simplest measurements you can make of the "size" of a compact symplectic manifold X is its Gromov width that measures the capacity of the largest ball that embeds into it. More generally, one can study the size of the largest ellipsoid of a given eccentricity that embeds into X. This function of the eccentricity has been (partially) calculated for certain 4-dimensional targets, such as the 4-ball or its one-point blowup, and turns out to have intricate arithmetic properties. This talk, which will be aimed at a nonspecialized audience, will describe some recent work with Nicki Magill and Morgan Weiler about the properties of this function when the target is a ball that has been blown up once with weight b.