Singularities, Mirror Symmetry, and the Gauged Linear Sigma Model
About this Title
Tyler J. Jarvis, Brigham Young University, Provo, UT and Nathan Priddis, Brigham Young University, Provo, UT, Editors
Publication: Contemporary Mathematics
Publication Year: 2021; Volume 763
ISBNs: 978-1-4704-5700-6 (print); 978-1-4704-6419-6 (online)
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.
Graduate students and research mathematicians interested in enumerative geometry, singularity theory, and the relations between algebraic geometry and mathematical physics.
Table of Contents
- Rachel Webb – Quasimaps and some examples of stacks for everybody
- Emily Clader – Introduction to the gauged linear sigma model
- Dustin Ross – Localization and mirror symmetry
- Wei-Ping Li – A brief introduction to cosection localization and $P$-fields
- Mark Shoemaker – Virtual classes for hypersurfaces via two-periodic complexes
- Jeongseok Oh – Localized Chern characters for 2-periodic complexes and virtual cycles
- Todor Milanov – Singularity theory and mirror symmetry
- Ursula Whitcher – Counting points with Berglund–Hübsch–Krawitz mirror symmetry
- Honglu Fan and Yuan-Pin Lee – Variations on the theme of quantum Lefschetz
- Rongxiao Mi – Type II extremal transitions in Gromov-Witten theory
- Chiu-Chu Melissa Liu – A lecture on holomorphic anomaly equations and extended holomorphic anomaly equations