Algebraic Geometry: Salt Lake City 2015
About this Title
Tomasso 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 97.2
ISBNs: 978-1-4704-3578-3 (print); 978-1-4704-4680-2 (online)
This is Part 2 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
- David Ben-Zvi and David Nadler – Betti Geometric Langlands
- Bhargav Bhatt – Specializing varieties and their cohomology from characteristic $0$ to characteristic $p$
- T. D. Browning – How often does the Hasse principle hold?
- Lucia Caporaso – Tropical methods in the moduli theory of algebraic curves
- Renzo Cavalieri, Paul Johnson, Hannah Markwig and Dhruv Ranganathan – A graphical interface for the Gromov-Witten theory of curves
- Hélène Esnault – Some fundamental groups in arithmetic geometry
- Laurent Fargues – From local class field to the curve and vice versa
- Mark Gross and Bernd Siebert – Intrinsic mirror symmetry and punctured Gromov-Witten invariants
- Eric Katz, Joseph Rabinoff and David Zureick-Brown – Diophantine and tropical geometry, and uniformity of rational points on curves
- Kiran S. Kedlaya and Jonathan Pottharst – On categories of $(\varphi , \Gamma )$-modules
- Minhyong Kim – Principal bundles and reciprocity laws in number theory
- B. Klingler, E. Ullmo and A. Yafaev – Bi-algebraic geometry and the André-Oort conjecture
- Max Lieblich – Moduli of sheaves: A modern primer
- Johannes Nicaise – Geometric invariants for non-archimedean semialgebraic sets
- Tony Pantev and Gabriele Vezzosi – Symplectic and Poisson derived geometry and deformation quantization
- Alena Pirutka – Varieties that are not stably rational, zero-cycles and unramified cohomology
- Takeshi Saito – On the proper push-forward of the characteristic cycle of a constructible sheaf
- Tamás Szamuely and Gergely Zábrádi – The $p$-adic Hodge decomposition according to Beilinson
- Akio Tamagawa – Specialization of $\ell $-adic representations of arithmetic fundamental groups and applications to arithmetic of abelian varieties
- Olivier Wittenberg – Rational points and zero-cycles on rationally connected varieties over number fields