By physical considerations, Huang, Katz and Klemm conjectured in 2015 that topological string partition functions for elliptic Calabi-Yau 3-folds are governed by certain Jacobi forms. This gives strong structure results for curve counting invariants of elliptic CY 3-folds.
Algebraic Geometry Seminar
The Algebraic Geometry Seminar features talks on all branches of algebraic geometry, as well as related research fields including, and not limited to: number theory, complex geometry, and differential geometry.
Many questions about Riemann surfaces are related to study their flat structures induced from abelian differentials. Loci of abelian differentials with prescribed type of zeros form a natural stratification.
For toric varieties there is a dictionary relating the geometry of divisors to the theory of polytopes. I will discuss how certain aspects of this dictionary can be extended to divisors on arbitrary smooth projective varieties.
A very old problem asks for the degree of a variety defined by rank conditions on matrices. The story of the modern approach begins in the 1970's, when Kempf and Laksov proved that the degeneracy locus for a map of vector bundles is given by a certain determinant in their Chern classes.
Ohio State University
I will discuss a general framework using Artin fans -- certain logarithmic algebraic stacks -- in which to understand the relationship between logarithmic stable maps and tropical curve counting.