A theory of stacks with twisted fields and its applications
The moduli spaces of stable maps play an important role in the Gromov-Witten theory. These moduli spaces, however, can be arbitrarily singular; their desingularization motivated us to introduce a theory of stacks with twisted fields, which can be applied to the resolution of the stable map moduli of genus 1 and 2 and possibly of arbitrary genus. In this talk, I will focus on the construction of the stacks with twisted fields. This is based on joint works with Yi Hu.