Hardcover ISBN:  9781470435578 
Product Code:  PSPUM/95 
370 pp 
List Price:  $126.00 
MAA Member Price:  $113.40 
AMS Member Price:  $100.80 
Electronic ISBN:  9781470441210 
Product Code:  PSPUM/95.E 
370 pp 
List Price:  $126.00 
MAA Member Price:  $113.40 
AMS Member Price:  $100.80 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 95; 2017MSC: Primary 14; 13; 19; 37;
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 farreaching 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.ReadershipGraduate students and researchers interested in new directions in algebraic geometry.

Table of Contents

Articles

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


Additional Material

Request Review Copy

Get Permissions
 Book Details
 Table of Contents
 Additional Material

 Request Review Copy
 Get Permissions
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 farreaching 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.

Articles

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