Mapping the Phase Space of toric Calabi-Yau 3-folds using Explainable Machine Learning

This talk will give a brief introduction on how bipartite graphs on a torus represent 4-dimensional quiver gauge theories and their moduli space which is a toric Calabi-Yau 3-fold - a cone over a Sasaki-Einstein 5-manifold. Under mirror symmetry, the bipartite graph can be identified with the tropical projection of the mirror curve obtained from the Newton polytope associated to the toric Calabi-Yau 3-fold. Changes to the complex structure moduli of the mirror Calabi-Yau determine the overall shape of the bipartite graph on the torus. For certain choices of complex structure moduli, the bipartite graph undergoes a graph mutation which is identified with Seiberg duality of the associated 4-dimensional quiver gauge theory. This talk will discuss recent progress in understanding when such mutations occur from the point of view of Calabi-Yau mirror symmetry with the help of new computational techniques such as machine learning.