Orbifold Gromov-Witten Theory

In this article, we introduce the notion of good map and use it to establish Gromov-Witten theory for orbifolds.Comment: Late

Twisted Orbifold K-Theory

We use equivariant methods to establish basic properties of orbifold K-theory. We introduce the notion of twisted orbifold K-theory in the presence of discrete torsion, and show how it can be explicitly computed for global quotients.Comment: 30 page

Orbifold Quantum Cohomology

This is a research announcement of the theory of orbifold quantum cohomology.Comment: Revised version, adding more reference

LG/CY correspondence: the state space isomorphism

We prove the classical mirror symmetry conjecture for the mirror pairs constructed by Berglund, H\"ubsch, and Krawitz. Our main tool is a cohomological LG/CY correspondence which provides a degree-preserving isomorphism between the cohomology of finite quotients of Calabi-Yau hypersurfaces inside a weighted projective space and the Fan-Jarvis-Ruan-Witten state space of the associated Landau-Ginzburg singularity theory.Comment: 37 pages, 9 figure