Surveys on Recent Developments in Algebraic Geometry


Author: Izzet Coskun,Tommaso de Fernex,Angela Gibney
Publisher: American Mathematical Soc.
ISBN: 1470435578
Category: $K$-theory -- Higher algebraic $K$-theory -- $Q$- and plus-constructions
Page: 370
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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 far-reaching 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 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.

Noncommutative Motives


Author: Gonçalo Tabuada
Publisher: American Mathematical Soc.
ISBN: 1470423979
Category: Algebraic varieties
Page: 114
View: 8957

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The theory of motives began in the early 1960s when Grothendieck envisioned the existence of a "universal cohomology theory of algebraic varieties". The theory of noncommutative motives is more recent. It began in the 1980s when the Moscow school (Beilinson, Bondal, Kapranov, Manin, and others) began the study of algebraic varieties via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a "universal invariant of noncommutative algebraic varieties". This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts. The first part, which is of independent interest, is devoted to the study of DG categories from a homotopical viewpoint. The second part, written with an emphasis on examples and applications, covers the theory of noncommutative pure motives, noncommutative standard conjectures, noncommutative motivic Galois groups, and also the relations between these notions and their commutative counterparts. The last part is devoted to the theory of noncommutative mixed motives. The rigorous formalization of this latter theory requires the language of Grothendieck derivators, which, for the reader's convenience, is revised in a brief appendix.

New Directions in Homotopy Theory


Author: Nitya Kitchloo, Mona Merling,Jack Morava,Emily Riehl,W. Stephen Wilson
Publisher: American Mathematical Soc.
ISBN: 1470437740
Category: Homotopy theory
Page: 194
View: 8548

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This volume contains the proceedings of the Second Mid-Atlantic Topology Conference, held from March 12–13, 2016, at Johns Hopkins University in Baltimore, Maryland. The focus of the conference, and subsequent papers, was on applications of innovative methods from homotopy theory in category theory, algebraic geometry, and related areas, emphasizing the work of younger researchers in these fields.

Arithmetic Noncommutative Geometry


Author: Matilde Marcolli
Publisher: American Mathematical Soc.
ISBN: 9780821882931
Category: Mathematics
Page: 136
View: 9637

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Arithmetic noncommutative geometry uses ideas and tools from noncommutative geometry to address questions in a new way and to reinterpret results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at Archimedean places of arithmetic surfaces and varieties. Noncommutative geometry can be expected to say something about topics of arithmetic interest because it provides the right framework for which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry. With a foreword written by Yuri Manin and a brief introduction to noncommutative geometry, this book offers a comprehensive account of the cross fertilization between two important areas, noncommutative geometry and number theory. It is suitable for graduate students and researchers interested in these areas

Quantum Interaction

8th International Conference, QI 2014, Filzbach, Switzerland, June 30 -- July 3, 2014. Revised Selected Papers
Author: Harald Atmanspacher,Claudia Bergomi,Thomas Filk,Kirsty Kitto
Publisher: Springer
ISBN: 3319159313
Category: Computers
Page: 283
View: 4917

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This book constitutes the refereed proceedings of the 8th International Conference on Quantum Interaction, QI 2014, held in Filzbach, Switzerland, in June/July 2014. The 19 papers together with 20 invited keynotes presented in this book were carefully selected from 22 submissions. Quantum Interaction has developed into an emerging interdisciplinary area of science combining research topics in fundamental issues, semantic and memory, decision making, games, politics and social aspects, non-locality and entanglement.

Theoretische Konzepte der Physik

Eine alternative Betrachtung
Author: Malcolm S. Longair
Publisher: Springer-Verlag
ISBN: 3642761119
Category: Science
Page: 380
View: 2763

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"Dies ist kein Lehrbuch der theoretischen Physik, auch kein Kompendium der Physikgeschichte ... , vielmehr eine recht anspruchsvolle Sammlung historischer Miniaturen zur Vergangenheit der theoretischen Physik - ihrer "Sternstunden", wenn man so will. Frei vom Zwang, etwas Erschöpfendes vorlegen zu müssen, gelingt dem Autor etwas Seltenes: einen "lebendigen" Zugang zum Ideengebäude der modernen Physik freizulegen, ... zu zeigen, wie Physik in praxi entsteht... Als Vehikel seiner Absichten dienen dem Autor geschichtliche Fallstudien, insgesamt sieben an der Zahl. Aus ihnen extrahiert er das seiner Meinung nach Lehrhafte, dabei bestrebt, mathematische Anachronismen womöglich zu vermeiden... Als Student hätte ich mir diese gescheiten Essays zum Werden unserer heutigen physikalischen Weltsicht gewünscht. Sie sind originell, didaktisch klug und genieren sich auch nicht, von der Faszination zu sprechen, die ... von der Physik ausgeht. Unnötig darauf hinzuweisen, das sie ein gründliches "konventionelles" Studium weder ersetzen wollen noch können, sie vermögen aber, dazu zu ermuntern." #Astronomische Nachrichten (zur englischen Ausgabe)#1

Gedankenmaterie


Author: Jean-Pierre Changeux,Alain Connes
Publisher: Springer-Verlag
ISBN: 3662073943
Category: Science
Page: 175
View: 9071

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Lectures on Fluid Dynamics

A Particle Theorist's View of Supersymmetric, Non-Abelian, Noncommutative Fluid Mechanics and D-Branes
Author: Roman Jackiw
Publisher: Springer Science & Business Media
ISBN: 9780387954226
Category: Science
Page: 114
View: 9888

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t/c with MS