Geometry and Physics Seminar: Gabriel Kerr

Homological mirror symmetry initially concerned Calabi-Yau 3-folds and, from that point, rapidly expanded to incorporate local Calabi-Yau's and Fano varieties. In this talk, I will discuss joint work with Ludmil Katzarkov and Maxim Kontsevich on extending this correspondence further to include quasi-affine toric varieties, the most basic example of which is a punctured plane. The complex side of the correspondence, or B-model, remains the derived category of coherent sheaves of the variety. On the mirror side, the A-model is a partially wrapped Fukaya category on the cotangent bundle of the torus. The key ingredient is the wrapping Hamiltonian which is defined as a distance^2 function away from a mirror non-compact Lagrangian skeleton. I will explain the geometric intuition for the case of the punctured plane and discuss elements of the proof for the general case.