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
View: 3615

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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: 5348

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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: 4544

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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: 1726

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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: 6284

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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.

Eure Väter, wo sind sie? Und die Propheten, leben sie ewig?

Roman
Author: Dave Eggers
Publisher: Kiepenheuer & Witsch
ISBN: 3462309188
Category: Fiction
Page: 224
View: 5256

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Nach dem Nr.-1-Bestseller »Der Circle« der neue Roman von Dave Eggers In »Der Circle« entwarf Dave Eggers das düstere Szenario einer durch und durch digitalisierten Welt. In seinem neuen Roman, der in der kalifornischen Wüste spielt, erörtert seine Hauptfigur die brennendsten Fragen unserer Zeit. Thomas ist ein Getriebener, der Antworten sucht. Antworten auf die Fragen, die er sich als junger weißer Amerikaner, der aus vielen Rastern fällt, stellt. Und Thomas hat nur ein Mittel, diese Antworten zu finden: Er fragt. Er entführt nach und nach Menschen in eine stillgelegte Militäranlage weit ab von der Zivilisation, kettet sie dort in alten Baracken an und fragt. Fragt einen Astronauten, warum er nie zum Mars geflogen ist. Fragt einen Kongressabgeordneten, wie er die Zukunft des Landes sieht. Fragt seine Mutter, warum sie ihn auf ein Leben vorbereitet hat, das nicht existiert. Und er fragt, warum sein Freund Don unschuldig sterben musste. Thomas gerät immer tiefer in den Strudel der Sinnfrage, bis er den Verstand vollkommen zu verlieren droht. In manchmal sokratisch anmutenden Dialogen lässt Dave Eggers diesen verzweifelten jungen Amerikaner von der Leine, der herausfinden will, worin seine Aufgabe auf diesem Planeten besteht. Dabei werden all die großen Fragen unseres Daseins gestellt, während die sprichwörtliche Bombe tickt.

Mathematical Aspects of Quantization

Center for Mathematics at Notre Dame, Summer School and Conference, May 31-June 10, 2011, Notre Dame University, Notre Dame, Indiana
Author: Sam Evens
Publisher: American Mathematical Soc.
ISBN: 0821875736
Category: Mathematics
Page: 308
View: 2141

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This book is a collection of expository articles from the Center of Mathematics at Notre Dame's 2011 program on quantization. Included are lecture notes from a summer school on quantization on topics such as the Cherednik algebra, geometric quantization, detailed proofs of Willwacher's results on the Kontsevich graph complex, and group-valued moment maps. This book also includes expository articles on quantization and automorphic forms, renormalization, Berezin-Toeplitz quantization in the complex setting, and the commutation of quantization with reduction, as well as an original article on derived Poisson brackets. The primary goal of this volume is to make topics in quantization more accessible to graduate students and researchers.

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: 7719

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t/c with MS