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Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
Motivic Integration
This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since.
Encyclopedia of Tidepools and Rocky Shores
"This is the book I have been waiting for! Written by experts in each field, this Encyclopedia provides a wealth of information not only about the tidepool and shore life but also the oceanography associated with these habitats. This will be a major reference guide for years to come."--Dr. Nigella Hillgarth, Executive Director, Birch Aquarium at Scripps, Scripps Institution of Oceanography "The "Encyclopedia of Tidepools and Rocky Shores" covers much more than one might guess. It ranges from oceanography, to physiology, biomechanics, and conservation science, along with the expected treatment of the diverse groups of organisms that live in those habitats. The coverage of each topic is kept s...
Berkovich Spaces and Applications
We present an introduction to Berkovich’s theory of non-archimedean analytic spaces that emphasizes its applications in various fields. The first part contains surveys of a foundational nature, including an introduction to Berkovich analytic spaces by M. Temkin, and to étale cohomology by A. Ducros, as well as a short note by C. Favre on the topology of some Berkovich spaces. The second part focuses on applications to geometry. A second text by A. Ducros contains a new proof of the fact that the higher direct images of a coherent sheaf under a proper map are coherent, and B. Rémy, A. Thuillier and A. Werner provide an overview of their work on the compactification of Bruhat-Tits building...
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
A Tale of One City
Piotrkow Trybunalski contained one of the oldest Jewish communities in Poland. In this large compilation of essays, the city is described during various periods of its history, with a special emphasis on the last 150 years. With contributions from many authors, most of them survivors, the volume gives a multifaceted picture of life as it was lived in a typical Jewish community before the Holocaust.
The Philosophy of Steven Soderbergh
“Provocative, insightful, and instructive analysis of the cinematic and philosophical significance of Steven Soderbergh’s work.” —Jason Holt, editor of The Daily Show and Philosophy: Moments of Zen in the Art of Fake News Widely regarded as a turning point in American independent cinema, Steven Soderbergh's sex, lies, and videotape launched the career of its twenty-six-year-old director, whose debut film was nominated for an Academy Award and went on to win the Cannes Film Festival’s top award, the Palme d’Or. The Philosophy of Steven Soderbergh breaks new ground by investigating salient philosophical themes through the unique story lines and innovative approaches to filmmaking that distinguish this celebrated artist. Editors R. Barton Palmer and Steven M. Sanders have brought together leading scholars in philosophy and film studies for the first systematic analysis of Soderbergh’s entire body of work, offering the first in-depth exploration of the philosophical ideas that form the basis of the work of one of the most commercially successful and consistently inventive filmmakers of our time.
Nonarchimedean and Tropical Geometry
This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-...
$p$-adic Geometry
"In recent decades, p-adic geometry and p-adic cohomology theories have become indispensable tools in number theory, algebraic geometry, and the theory of automorphic representations. The Arizona Winter Schoo1 2007, on which the current book is based, was a unique opportunity to introduce graduate students to this subject." "Following invaluable introductions by John Tate and Vladimir Berkovich, two pioneers of non-archimedean geometry, Brian Conrad's chapter introduces the general theory of Tate's rigid analytic spaces, Raynaud's view of them as the generic fibers of formal schemes, and Berkovich spaces. Samit Dasgupta and Jeremy Teitelbaum discuss the p-adic upper half plane as an example ...
