This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. It contains a great deal of information not fully covered in the published literature and showcases the current state of the art in orbital string theory. The subject of orbifolds has a long prehistory, going back to the work of Thurston and Haefliger, with roots in the theory of manifolds, group actions, and foliations. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory.The present volume presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. By presenting the work of a broad range of mathematicians and physicists who use and study orbifolds, it familiarizes readers with the various points of view and types of results the researchers bring to the subject.
Algebraic orbifold quantum products by D. Abramovich, T. Graber, and A. Vistoli Orbifold Gromov-Witten theory by W. Chen and Y. Ruan On orbifold elliptic genus by C. Dong, K. Liu, and X. Ma Open-string Gromov-Witten invariants: Calculations and a mirror "theorem" by T. Graber and E. Zaslow Orbifold quantum cohomology of the classifying space of a finite group by T. J. Jarvis and T. Kimura Orbifold Frobenius algebras, cobordisms and monodromies by R. M. Kaufmann Loop groupoids, Gerbes, and twisted sectors on orbifolds by E. Lupercio and B. Uribe Framed knots at large $N$ by M. Marino and C. Vafa Orbifolds as groupoids: An introduction by I. Moerdijk Orbifold cohomology group of toric varieties by M. Poddar Hilbert schemes and symmetric products: A dictionary by Z. Qin and W. Wang Stringy orbifolds by Y. Ruan Discrete torsion, quotient stacks, and string orbifolds by E. Sharpe Orbifold constructions of $K3$: A link between conformal field theory and geometry by K. Wendland.