• 01/07/2019: Polarized tropical manifolds and Lagrangian torus fibrations
• 01/09/2019: Conifold transitions and deformations of polarized tropical manifolds

January 7, 2019
TITLE: Polarized tropical manifolds and Lagrangian torus fibrations

ABSTRACT: I will review the notion of polarized tropical manifolds which are the basic combinatorial objects in the Gross-Siebert program. These can be viewed as the basis of a Lagrangian torus fibration on a symplectic Calabi-Yau manifold, but via the Legendre tranfsform they also provide the starting data for the reconstruction of the mirror family using the Gross-Siebert algorithm.

January 9, 2019
TITLE: Conifold transitions and deformations of polarized tropical manifolds

ABSTRACT: Conifold singularities have a nice description in terms of polarized tropical manifolds. I will describe a result where the obstructions to the existence of symplectic resolutions (Smith-Thomas-Yau) and of the complex smoothings on the mirror (Friedman-Tian) can be both read in terms of certain tropical cycles. This suggests an approach, via the Gross-Siebert program, to Morrison’s Conjecture stating that the mirror of a resolution is a smoothing of the mirror. In a joint work with Helge Ruddat this idea leads to the notion of a deformation of a polarized tropical manifold induced by a tropical cycle.