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.
B. Lehmann, A snapshot of the Minimal Model Program
Z. Patakfalvi, K. Schwede, and K. Tucker, Positive characteristic algebraic
geometry
O. Tommasi, The geometry of the moduli space of curves and abelian varieties
J. Huizenga, Birational geometry of moduli spaces of sheaves and Bridgeland
stability
E. Clader, Gromov-Witten theory: From curve counts to string theory
D. Chen, Teichmuller dynamics in the eyes of an algebraic geometer
A. Auel and M. Bernardara, Cycles, derived categories, and rationality
C. Robles, Degenerations of Hodge structure
D. Erman and S. V. Sam, Questions about Boij-Soderberg theory
B. Antieau and E. Elmanto, A primer for unstable motivic homotopy theory.
Izzet Coskun, University of Illinois at Chicago, IL.
Tommaso de Fernex, University of Utah, Salt Lake City, UT.
Angela Gibney, University of Georgia, Athens, GA.
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