Cyclic Coverings Calabi Yau Manifolds And Complex Multiplication

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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication

Christian Rohde
Cyclic Coverings Calabi Yau Manifolds and Complex Multiplication Book PDF

Author : Christian Rohde
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 40,9 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9783642006388

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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication by Christian Rohde Pdf

The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line are computed for a broad range of examples.

Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

Radu Laza,Matthias Schütt,Noriko Yui
Arithmetic and Geometry of K3 Surfaces and Calabi Yau Threefolds Book PDF

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 48,7 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461464037

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Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds by Radu Laza,Matthias Schütt,Noriko Yui Pdf

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

String-Math 2015

Si Li,Bong H. Lian, Wei Song,Shing-Tung Yau
String Math 2015 Book PDF

Author : Si Li,Bong H. Lian, Wei Song,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 42,8 Mb
Release : 2017-11-28
Category : Algebraic geometry -- Projective and enumerative geometry -- Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
ISBN : 9781470429515

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String-Math 2015 by Si Li,Bong H. Lian, Wei Song,Shing-Tung Yau Pdf

This volume contains the proceedings of the conference String-Math 2015, which was held from December 31, 2015–January 4, 2016, at Tsinghua Sanya International Mathematics Forum in Sanya, China. Two of the main themes of this volume are frontier research on Calabi-Yau manifolds and mirror symmetry and the development of non-perturbative methods in supersymmetric gauge theories. The articles present state-of-the-art developments in these topics. String theory is a broad subject, which has profound connections with broad branches of modern mathematics. In the last decades, the prosperous interaction built upon the joint efforts from both mathematicians and physicists has given rise to marvelous deep results in supersymmetric gauge theory, topological string, M-theory and duality on the physics side, as well as in algebraic geometry, differential geometry, algebraic topology, representation theory and number theory on the mathematics side.

Recent Advances in Hodge Theory

Matt Kerr,Gregory Pearlstein
Recent Advances in Hodge Theory Book PDF

Author : Matt Kerr,Gregory Pearlstein
Publisher : Cambridge University Press
Page : 533 pages
File Size : 53,8 Mb
Release : 2016-02-04
Category : Mathematics
ISBN : 9781107546295

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Recent Advances in Hodge Theory by Matt Kerr,Gregory Pearlstein Pdf

Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

Modular And Automorphic Forms & Beyond

Hossein Movasati
Modular And Automorphic Forms Beyond Book PDF

Author : Hossein Movasati
Publisher : World Scientific
Page : 323 pages
File Size : 54,9 Mb
Release : 2021-10-12
Category : Mathematics
ISBN : 9789811238697

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Modular And Automorphic Forms & Beyond by Hossein Movasati Pdf

The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.

Periods And Special Functions In Transcendence

Tretkoff Paula B
Periods And Special Functions In Transcendence Book PDF

Author : Tretkoff Paula B
Publisher : World Scientific
Page : 228 pages
File Size : 53,5 Mb
Release : 2017-05-04
Category : Mathematics
ISBN : 9781786342966

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Periods And Special Functions In Transcendence by Tretkoff Paula B Pdf

This book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi–Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.

Mumford-Tate Groups and Domains

Mark Green,Phillip A. Griffiths,Matt Kerr
Mumford Tate Groups and Domains Book PDF

Author : Mark Green,Phillip A. Griffiths,Matt Kerr
Publisher : Princeton University Press
Page : 298 pages
File Size : 54,8 Mb
Release : 2012-04-22
Category : Mathematics
ISBN : 9781400842735

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Mumford-Tate Groups and Domains by Mark Green,Phillip A. Griffiths,Matt Kerr Pdf

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.

The Use of Ultraproducts in Commutative Algebra

Hans Schoutens
The Use of Ultraproducts in Commutative Algebra Book PDF

Author : Hans Schoutens
Publisher : Springer
Page : 210 pages
File Size : 50,8 Mb
Release : 2010-07-16
Category : Mathematics
ISBN : 9783642133688

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The Use of Ultraproducts in Commutative Algebra by Hans Schoutens Pdf

In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.

Geometric Theory of Discrete Nonautonomous Dynamical Systems

Christian Pötzsche
Geometric Theory of Discrete Nonautonomous Dynamical Systems Book PDF

Author : Christian Pötzsche
Publisher : Springer
Page : 399 pages
File Size : 51,9 Mb
Release : 2010-08-24
Category : Mathematics
ISBN : 9783642142581

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Geometric Theory of Discrete Nonautonomous Dynamical Systems by Christian Pötzsche Pdf

Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.

Topics in Algebraic and Topological K-Theory

Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Topics in Algebraic and Topological K Theory Book PDF

Author : Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Publisher : Springer
Page : 308 pages
File Size : 53,9 Mb
Release : 2010-10-28
Category : Mathematics
ISBN : 9783642157080

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Topics in Algebraic and Topological K-Theory by Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën Pdf

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

The Analysis of Fractional Differential Equations

Kai Diethelm
The Analysis of Fractional Differential Equations Book PDF

Author : Kai Diethelm
Publisher : Springer
Page : 247 pages
File Size : 49,6 Mb
Release : 2010-08-18
Category : Mathematics
ISBN : 9783642145742

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The Analysis of Fractional Differential Equations by Kai Diethelm Pdf

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Séminaire de Probabilités XLIII

Catherine Donati Martin,Antoine Lejay,Alain Rouault
S minaire de Probabilit s XLIII Book PDF

Author : Catherine Donati Martin,Antoine Lejay,Alain Rouault
Publisher : Springer
Page : 503 pages
File Size : 52,8 Mb
Release : 2010-10-20
Category : Mathematics
ISBN : 9783642152177

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Séminaire de Probabilités XLIII by Catherine Donati Martin,Antoine Lejay,Alain Rouault Pdf

This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.

Morrey and Campanato Meet Besov, Lizorkin and Triebel

Wen Yuan,Winfried Sickel,Dachun Yang
Morrey and Campanato Meet Besov Lizorkin and Triebel Book PDF

Author : Wen Yuan,Winfried Sickel,Dachun Yang
Publisher : Springer
Page : 288 pages
File Size : 50,9 Mb
Release : 2010-09-02
Category : Mathematics
ISBN : 9783642146060

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Morrey and Campanato Meet Besov, Lizorkin and Triebel by Wen Yuan,Winfried Sickel,Dachun Yang Pdf

During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.

Computational Approach to Riemann Surfaces

Alexander I. Bobenko TU Berlin,Christian Klein
Computational Approach to Riemann Surfaces Book PDF

Author : Alexander I. Bobenko TU Berlin,Christian Klein
Publisher : Springer
Page : 264 pages
File Size : 40,7 Mb
Release : 2011-02-03
Category : Mathematics
ISBN : 9783642174131

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Computational Approach to Riemann Surfaces by Alexander I. Bobenko TU Berlin,Christian Klein Pdf

This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Symmetries of Compact Riemann Surfaces

Emilio Bujalance,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki
Symmetries of Compact Riemann Surfaces Book PDF

Author : Emilio Bujalance,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki
Publisher : Springer
Page : 164 pages
File Size : 53,9 Mb
Release : 2010-09-29
Category : Mathematics
ISBN : 9783642148286

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Symmetries of Compact Riemann Surfaces by Emilio Bujalance,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki Pdf

This monograph covers symmetries of compact Riemann surfaces. It examines the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.