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

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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.

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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.