Singularities, Mirror Symmetry, and the Gauged Linear Sigma Model (Contemporary Mathematics)

This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model. Most of the expository works are based on introductory lecture series given at the workshop and provide an approachable introduction for graduate students to some fundamental topics in mirror symmetry and singularity theory, including quasimaps, localization, the gauged linear sigma model (GLSM), virtual classes, cosection localization, $p$-fields, and Saito's primitive forms. These articles help readers bridge the gap from the standard graduate curriculum in algebraic geometry to exciting cutting-edge research in the field. The volume also contains several research articles by leading researchers, showcasing new developments in the field. Preface / Yongbin Ruan and Nathan Priddis -- Quasimaps and some examples of stacks for everyone / Rachel Webb -- Introduction to the gauged linear sigma model / Emily Clader -- Localization and mirror symmetry / Dustin Ross -- A brief introduction to cosection localization and p-fields / Wei-Ping Li -- Virtual classes for hypersurfaces via two-periodic complexes / Mark Shoemaker -- Localized Chern characters for 2-periodic complexes and virtual cycles / Jeongseok Oh -- Singularity theory and mirror symmetry / Todor Milanov -- Arithmetic mirror symmetry and hypergeometric structures / Ursula Whitcher -- Variations on the theme of quantum Lefschetz / Honglu Fan and Yuan-Pin Lee -- Extremal transitions and quantum D-modules / Rongxiao Mi -- A lecture on holomorphic anomaly equations and extended holomorphic anomaly equations / Chiu-Chu Melissa Liu Contains the proceedings of the workshop ‘Crossing the Walls in Enumerative Geometry’, held in May 2018. The volume features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model.