Speaker
Kyler Siegel, University of Southern California
Abstract
A central question in quantitative symplectic geometry asks when one ellipsoid can be symplectically embedded into another. The “stabilized ellipsoid embedding problem” offers an intriguing special case which serves as a bridge between known results in dimension four and terra incognita in higher dimensions. There is a known procedure for obstructing stabilized symplectic embeddings via SFT moduli spaces of punctured rational curves with one negative end, but constructing the requisite curves is quite difficult. In fact, we recently observed that these moduli spaces are directly related to classical questions about singular plane curves. In this talk I will explain how to solve these questions using nontrivial input from log Calabi-Yau mirror symmetry and quiver representation theory. In particular, we construct a large family of singular plane curves which realize the minimal possible degree for a curve carrying a (p,q) cusp. This is joint work in progress with D. McDuff.