On orbifold Gromov-Witten theory in small codimensions -- Hsian-Hua Tseng, October 16, 2015

For a Deligne-Mumford stack, it is known that stack structures in codimension 0 are given by gerbes. Geraschenko-Satriano proved that stack structures in codimension 1 are given by root constructions along divisors. It is also known that stack structures in codimension at least 2 are canonically determined by the coarse moduli scheme.

The purpose of this talk is to describe some attempts at understanding the Gromov-Witten theory of a given Deligne-Mumford stack in view of the codimension of its stack structures. More precisely, we will describe some conjectures and progress on Gromov-Witten theory of gerbes and of root stacks along divisors.