Tropical cycles and the tropological vertex
Seminar/Forum
Complex manifolds with normal crossing divisors, and normal crossing degenerations, have a natural large scale with a tropical, or piecewise integralaffine structure. I will discuss the case when some useful cohomology theories are described by tropical cycles in this tropical large scale. This case is of interest to me, because relative GromovWitten invariants of these spaces correspond to counts of tropical curves in this tropical large scale. If time permits, I will draw some pictures, and explain some beautiful aspects of this tropical correspondence in the CalabiYao 3fold setting, related to the Strominger—Yao—Zaslow approach to mirror symmetry: In this case, the large scale is a 3dimensional integral affine manifold with singularities along a 1dimensional graph. The vertices of this singular graph come in two types: positive and negative, and the relative Gromov—Witten invariants around the positive vertices contain the topological vertex of Aganagic, Klemm, Marino and Vafa.
Presenter

Dr Brett Parker, Monash University