Motivic Integration and Its Interactions with Model Theory and Non-Archimedean Geometry:

Motivic Integration and Its Interactions with Model Theory and Non-Archimedean Geometry: PDF Author: Raf Cluckers
Publisher:
ISBN: 9781139145350
Category : MATHEMATICS
Languages : en
Pages : 264

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Book Description
An overview of different theories of motivic integration and their applications.

Motivic Integration and Its Interactions with Model Theory and Non-Archimedean Geometry:

Motivic Integration and Its Interactions with Model Theory and Non-Archimedean Geometry: PDF Author: Raf Cluckers
Publisher:
ISBN: 9781139145350
Category : MATHEMATICS
Languages : en
Pages : 264

Get Book

Book Description
An overview of different theories of motivic integration and their applications.

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1 PDF Author: Raf Cluckers
Publisher: Cambridge University Press
ISBN: 1139499793
Category : Mathematics
Languages : en
Pages : 347

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Book Description
Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 2, which unite the several viewpoints and applications, will prove invaluable.

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1 PDF Author: Raf Cluckers
Publisher: Cambridge University Press
ISBN: 9780521149761
Category : Mathematics
Languages : en
Pages : 346

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Book Description
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 first volume contains introductory texts on the model theory of valued fields, different approaches to non-Archimedean geometry, and motivic integration on algebraic varieties and non-Archimedean spaces.

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2 PDF Author: Raf Cluckers
Publisher: Cambridge University Press
ISBN: 1139501739
Category : Mathematics
Languages : en
Pages : 263

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Book Description
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 and Its Interactions with Model Theory and Non-archimedean Geometry

Motivic Integration and Its Interactions with Model Theory and Non-archimedean Geometry PDF Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description


Facets of Algebraic Geometry: Volume 2

Facets of Algebraic Geometry: Volume 2 PDF Author: Paolo Aluffi
Publisher: Cambridge University Press
ISBN: 1108890547
Category : Mathematics
Languages : en
Pages : 396

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Book Description
Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.

Integrable Systems and Algebraic Geometry: Volume 2

Integrable Systems and Algebraic Geometry: Volume 2 PDF Author: Ron Donagi
Publisher: Cambridge University Press
ISBN: 1108805337
Category : Mathematics
Languages : en
Pages : 537

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Book Description
Created as a celebration of mathematical pioneer Emma Previato, this comprehensive second volume highlights the connections between her main fields of research, namely algebraic geometry and integrable systems. Written by leaders in the field, the text is accessible to graduate students and non-experts, as well as researchers.

Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents

Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents PDF Author: Kevin Broughan
Publisher: Cambridge University Press
ISBN: 1108195431
Category : Mathematics
Languages : en
Pages : 514

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Book Description
The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

Handbook of Geometry and Topology of Singularities IV

Handbook of Geometry and Topology of Singularities IV PDF Author: José Luis Cisneros-Molina
Publisher: Springer Nature
ISBN: 3031319257
Category : Mathematics
Languages : en
Pages : 622

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Book Description
This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Model Theory in Algebra, Analysis and Arithmetic

Model Theory in Algebra, Analysis and Arithmetic PDF Author: Lou van den Dries
Publisher: Springer
ISBN: 3642549365
Category : Mathematics
Languages : en
Pages : 201

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Book Description
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.