Surveys on Recent Developments in Algebraic Geometry
About this Title
Izzet Coskun, University of Illinois at Chicago, Chicago, IL, Tommaso de Fernex, University of Utah, Salt Lake City, UT and Angela Gibney, University of Georgia, Athens, GA, Editors
Publication: Proceedings of Symposia in Pure Mathematics
Publication Year: 2017; Volume 95
ISBNs: 978-1-4704-3557-8 (print); 978-1-4704-4121-0 (online)
The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah.
These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic $p$ and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
Graduate students and researchers interested in new directions in algebraic geometry.
Table of Contents
- Brian Lehmann – A snapshot of the Minimal Model Program
- Zsolt Patakfalvi, Karl Schwede and Kevin Tucker – Positive characteristic algebraic geometry
- Orsola Tommasi – The geometry of the moduli space of curves and abelian varieties
- Jack Huizenga – Birational geometry of moduli spaces of sheaves and Bridgeland stability
- Emily Clader – Gromov–Witten theory: From curve counts to string theory
- Dawei Chen – Teichmüller dynamics in the eyes of an algebraic geometer
- Asher Auel and Marcello Bernardara – Cycles, derived categories, and rationality
- Colleen Robles – Degenerations of Hodge structure
- Daniel Erman and Steven V Sam – Questions about Boij–Söderberg theory
- Benjamin Antieau and Elden Elmanto – A primer for unstable motivic homotopy theory