Hebrew University topology and geometry seminar

Abstract: Counting the number of curves in an algebraic variety is a classical topic in algebraic geometry. I will begin by backgrounds on enumerative geometry and motivations from mirror symmetry. Then I will explain how tropical geometry and non-archimedean geometry (Berkovich spaces) can help us. I will explain the construction of the moduli stack of non-archimedean stable maps based on a notion of non-archimedean Kähler structure. I will show an analog of Gromov's compactness theorem and discuss the tropicalization of the space of stable maps. If time permits, I will discuss an application to the enumeration of holomorphic discs and cylinders in log Calabi-Yau surfaces.