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Hardcover ISBN:  9781470435776 
Product Code:  PSPUM/97.1 
List Price:  $139.00 
MAA Member Price:  $125.10 
AMS Member Price:  $111.20 
eBook ISBN:  9781470446789 
Product Code:  PSPUM/97.1.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Hardcover ISBN:  9781470435776 
eBook ISBN:  9781470446789 
Product Code:  PSPUM/97.1.B 
List Price:  $274.00 $206.50 
MAA Member Price:  $246.60 $185.85 
AMS Member Price:  $219.20 $165.20 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 97; 2018; 655 ppMSC: Primary 14; 53;
This is Part 1 of a twovolume 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.
ReadershipGraduate students and researchers working in algebraic geometry and its applications.
This item is also available as part of a set: 
Table of Contents

Part 1

Arend Bayer  Wallcrossing implies BrillNoether: Applications of stability conditions on surfaces

Robert J. Berman  Kähler–Einstein metrics, canonical random point processes and birational geometry

Tom Bridgeland  Hall algebras and DonaldsonThomas invariants

Serge Cantat  The Cremona group

AnaMaria Castravet  Mori dream spaces and blowups

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 higherdimensional minimal varieties

Christopher D. Hacon, James McKernan and Chenyang Xu  Boundedness of varieties of log general type

Daniel HalpernLeistner  $\Theta $stratifications, $\Theta $reductive stacks, and applications

Andreas Höring and Thomas Peternell  Bimeromorphic geometry of Kähler threefolds

Sándor J. Kovács  Moduli of stable logvarieties—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  Noncommutative deformations and DonaldsonThomas invariants

Valentino Tosatti  Nakamaye’s theorem on complex manifolds


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This is Part 1 of a twovolume 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.

Part 1

Arend Bayer  Wallcrossing implies BrillNoether: Applications of stability conditions on surfaces

Robert J. Berman  Kähler–Einstein metrics, canonical random point processes and birational geometry

Tom Bridgeland  Hall algebras and DonaldsonThomas invariants

Serge Cantat  The Cremona group

AnaMaria Castravet  Mori dream spaces and blowups

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 higherdimensional minimal varieties

Christopher D. Hacon, James McKernan and Chenyang Xu  Boundedness of varieties of log general type

Daniel HalpernLeistner  $\Theta $stratifications, $\Theta $reductive stacks, and applications

Andreas Höring and Thomas Peternell  Bimeromorphic geometry of Kähler threefolds

Sándor J. Kovács  Moduli of stable logvarieties—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  Noncommutative deformations and DonaldsonThomas invariants

Valentino Tosatti  Nakamaye’s theorem on complex manifolds