Bücher der Reihe Simons Symposia

Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

This proceedings volume contains articles related to the research presented at the 2017 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning integral questions and their connections to notions in algebraic topology.

Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013.¿Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classification of psuedoeffective codimension one distributions.Foliations play a fundamental role in algebraic geometry, for example in the proof of abundance for threefolds and to a solution of the Green-Griffiths conjecture for surfaces of general type with positive Segre class. The purpose of this volume is to foster communication and enable interactions between experts who work on holomorphic foliations and birational geometry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study.

Thisvolume grew out of two Simons Symposia on "Nonarchimedean and tropicalgeometry" which took place on the island of St. John in April 2013 and inPuerto Rico in February 2015. Each meeting gathered a small group of expertsworking near the interface between tropical geometry and nonarchimedeananalytic spaces for a series of inspiring and provocative lectures on cuttingedge research, interspersed with lively discussions and collaborative work insmall groups. The articles collected here, which include high-level surveys aswell as original research, mirror the main themes of the two Symposia.Topicscovered in this volume include: Differential forms and currents, andsolutions of Monge-Ampere type differential equations on Berkovich spaces andtheir skeletons; The homotopy types of nonarchimedean analytifications;The existence of "faithful tropicalizations" which encode the topology andgeometry of analytifications;Relations between nonarchimedean analyticspaces and algebraic geometry, including logarithmic schemes, birationalgeometry, and the geometry of algebraic curves;Extended notions oftropical varieties which relate to Huber's theory of adic spaces analogously tothe way that usual tropical varieties relate to Berkovich spaces; and Relationsbetween nonarchimedean geometry and combinatorics, including deep andfascinating connections between matroid theory, tropical geometry, and Hodgetheory.

Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory.

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems.

Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classification of psuedoeffective codimension one distributions.Foliations play a fundamental role in algebraic geometry, for example in the proof of abundance for threefolds and to a solution of the Green-Griffiths conjecture for surfaces of general type with positive Segre class. The purpose of this volume is to foster communication and enable interactions between experts who work on holomorphic foliations and birational geometry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study.

Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory.

Thisvolume grew out of two Simons Symposia on "Nonarchimedean and tropicalgeometry" which took place on the island of St. John in April 2013 and inPuerto Rico in February 2015. Each meeting gathered a small group of expertsworking near the interface between tropical geometry and nonarchimedeananalytic spaces for a series of inspiring and provocative lectures on cuttingedge research, interspersed with lively discussions and collaborative work insmall groups. The articles collected here, which include high-level surveys aswell as original research, mirror the main themes of the two Symposia.Topicscovered in this volume include: Differential forms and currents, andsolutions of Monge-Ampere type differential equations on Berkovich spaces andtheir skeletons; The homotopy types of nonarchimedean analytifications;The existence of "faithful tropicalizations" which encode the topology andgeometry of analytifications;Relations between nonarchimedean analyticspaces and algebraic geometry, including logarithmic schemes, birationalgeometry, and the geometry of algebraic curves;Extended notions oftropical varieties which relate to Huber's theory of adic spaces analogously tothe way that usual tropical varieties relate to Berkovich spaces; and Relationsbetween nonarchimedean geometry and combinatorics, including deep andfascinating connections between matroid theory, tropical geometry, and Hodgetheory.

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems.

This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning non-abelian aspects This volume contains both original research articles as well as articles that contain both new research as well as survey some of these recent developments.