Title: A Combinatorial Gateway to Calabi-Yau Toric Geometry
| Speaker | Jesse Huang |
| Affiliation | University of Waterloo |
| Location | MC 6029 |
Abstract: The goal of this talk is to introduce Calabi-Yau toric geometry from a purely combinatorial perspective, through the rich structures carried by an embedded bipartite graph on a torus called a dimer model.
In the pre-talk, we will demonstrate how matchings, tilings, and quivers naturally encodes deep geometric and physical content. No background in algebraic geometry will be assumed; instead, we’ll build the story from the ground up, with an emphasis on visual intuition and discrete structures.
Next, I will discuss how dimer models simultaneously encode the data of a toric Calabi-Yau singularity and its mirror dual, unifying perspectives from the B-model and A-model of homological mirror symmetry through noncommutative algebras. We will proceed with some recent developments and open problems, including connections to the symplectic geometry of Landau-Ginzburg models and Van den Bergh’s noncommutative resolution conjecture for toric Gorenstein affine singularities. To conclude the talk, we will discuss an example of a higher dimensional generalization and its connection to my recent research works.
This talk is also partially based on two undergraduate research projects in the present semester, where we study variations of dimer models of the same lattice polygon from different choices in the fast inverse algorithm, and implications on the two sides of mirror symmetry:
- (DRP) Dimer Variation and Geometry of Landau-Ginzburg Models, with Kenneth Xiao and Elizabeth Cai (A-model)
- (NSERC USRA) Dimer Variation and NCCR Mutations, with Filip Mildrag and Elana Kalashnikov (B-model)
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.