Algebraic Geometry: Salt Lake City 2015
About this Title
Tommaso de Fernex, University of Utah, Salt Lake City, UT, Brendan Hassett, Brown University, Providence, RI, Mircea Mustaţă, University of Michigan, Ann Arbor, MI, Martin Olsson, University of California, Berkeley, CA, Mihnea Popa, Northwestern University, Evanston, IL and Richard Thomas, Imperial College of London, London, United Kingdom, Editors
Publication: Proceedings of Symposia in Pure Mathematics
Publication Year: 2018; Volume 97.1
ISBNs: 978-1-4704-3577-6 (print); 978-1-4704-4678-9 (online)
This is Part 1 of a two-volume set.
Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments.
The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic.
Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic $p$ and $p$-adic tools, etc. The resulting articles will be important references in these areas for years to come.
Graduate students and researchers working in algebraic geometry and its applications.
Table of Contents
- Arend Bayer – Wall-crossing implies Brill-Noether: Applications of stability conditions on surfaces
- Robert J. Berman – Kähler–Einstein metrics, canonical random point processes and birational geometry
- Tom Bridgeland – Hall algebras and Donaldson-Thomas invariants
- Serge Cantat – The Cremona group
- Ana-Maria Castravet – Mori dream spaces and blow-ups
- Tommaso de Fernex – The space of arcs of an algebraic variety
- Simon K. Donaldson – Stability of algebraic varieties and Kähler geometry
- Lawrence Ein and Robert Lazarsfeld – Syzygies of projective varieties of large degree: Recent progress and open problems
- Eduardo González, Pablo Solis and Chris T. Woodward – Stable gauged maps
- Daniel Greb, Stefan Kebekus and Behrouz Taji – Uniformisation of higher-dimensional minimal varieties
- Christopher D. Hacon, James McKernan and Chenyang Xu – Boundedness of varieties of log general type
- Daniel Halpern-Leistner – $\Theta $-stratifications, $\Theta $-reductive stacks, and applications
- Andreas Höring and Thomas Peternell – Bimeromorphic geometry of Kähler threefolds
- Sándor J. Kovács – Moduli of stable log-varieties—an update
- Andrei Okounkov – Enumerative geometry and geometric representation theory
- Rahul Pandharipande – A calculus for the moduli space of curves
- Zsolt Patakfalvi – Frobenius techniques in birational geometry
- Mihai Păun – Singular Hermitian metrics and positivity of direct images of pluricanonical bundles
- Mihnea Popa – Positivity for Hodge modules and geometric applications
- Richard P. Thomas – Notes on homological projective duality
- Yukinobu Toda – Non-commutative deformations and Donaldson-Thomas invariants
- Valentino Tosatti – Nakamaye’s theorem on complex manifolds