Calabi-Yau Moduli Spaces from 2D Gauge Theories

In this talk I will introduce methods to use 2d gauge theories as a means to describe Calabi-Yau varieties and their moduli spaces. As I review, this description furnishes a natural framework to predict derived equivalences between pairs of (sometimes even non-birational) Calabi-Yau varieties. A prominent example of this kind is realized by the Rødland non-birational pair of Calabi-Yau threefolds.
Using the 2d gauge theory description, I will propose further examples of derived equivalences among non-birational Calabi-Yau varieties.