Université Paris Diderot, Paris 7
Counting holomorphic cylinders via non-archimedean geometry
Counting the number of curves in an algebraic variety is a classical topic in algebraic geometry. Inspired by string theory and mirror symmetry, people started to look at not only closed curves, but also discs, cylinders, etc. In this talk, I will begin by presenting several beautiful historic results. Then I will explain how tropical geometry and non-archimedean analytic geometry enter the game of counting. If time permits, I will discuss a particular case of log Calabi–Yau surfaces, and explain its relations to the Kontsevich–Soibelman wall-crossing formula and the Gross–Siebert program.