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Compact Manifolds with Special Holonomy by Dominic D. Joyce Pdf
This is a combination of a graduate textbook on Reimannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It contains much new research and many new examples.
Riemannian Holonomy Groups and Calibrated Geometry by Dominic D. Joyce Pdf
Covering an exciting and active area of research at the crossroads of several different fields in mathematics and physics, and drawing on the author's previous work, this text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.
Special Metrics and Group Actions in Geometry by Simon G. Chiossi,Anna Fino,Emilio Musso,Fabio Podestà,Luigi Vezzoni Pdf
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
Lectures and Surveys on G2-Manifolds and Related Topics by Spiro Karigiannis,Naichung Conan Leung,Jason D. Lotay Pdf
This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.
Nearly Pseudo-Kähler Manifolds and Related Special Holonomies by Lars Schäfer Pdf
Developing and providing an overview of recent results on nearly Kähler geometry on pseudo-Riemannian manifolds, this monograph emphasizes the differences with the classical Riemannian geometry setting. The focal objects of the text are related to special holonomy and Killing spinors and have applications in high energy physics, such as supergravity and string theory. Before starting into the field, a self-contained introduction to the subject is given, aimed at students with a solid background in differential geometry. The book will therefore be accessible to masters and Ph.D. students who are beginning work on nearly Kähler geometry in pseudo-Riemannian signature, and also to non-experts interested in gaining an overview of the subject. Moreover, a number of results and techniques are provided which will be helpful for differential geometers as well as for high energy physicists interested in the mathematical background of the geometric objects they need.
Calabi-Yau Manifolds and Related Geometries by Mark Gross,Daniel Huybrechts,Dominic Joyce Pdf
This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results. From the reviews: "An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book." --MATHEMATICAL REVIEWS
Global Differential Geometry by Christian Bär,Joachim Lohkamp,Matthias Schwarz Pdf
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
"Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."
150 Years of Mathematics at Washington University in St. Louis by Gary R. Jensen,Steven George Krantz Pdf
Articles in this book are based on talks given at the conference commemorating the 150th anniversary of the Washington University in St. Louis. The articles cover a wide range of important topics in mathematics, and are written by former and present faculty or graduates of the Washington University Department of Mathematics. The volume is prefaced by a brief history of the Washington University Department of Mathematics, a roster of those who received the PhD degree from the department, and a list of the Washington University Department of Mathematics faculty.
Differential Geometry, Valencia 2001 by Olga Gil-Medrano Pdf
This volume presents the proceedings of a conference on differential geometry held in honour of the 60th birthday of A M Naveira. The meeting brought together distinguished researchers from a variety of areas in Riemannian geometry. The topics include: geometry of the curvature tensor, variational problems for geometric functionals such as WillmoreOCoChen tension, volume and energy of foliations and vector fields, and energy of maps. Many papers concern special submanifolds in Riemannian and Lorentzian manifolds, such as those with constant mean (scalar, Gauss, etc.) curvature and those with finite total curvature."
Differential Geometry, Valencia 2001 by Olga Gil-Medrano,Vicente Miquel Pdf
This volume presents the proceedings of a conference on differential geometry held in honour of the 60th birthday of A M Naveira. The meeting brought together distinguished researchers from a variety of areas in Riemannian geometry. The topics include: geometry of the curvature tensor, variational problems for geometric functionals such as Willmore–Chen tension, volume and energy of foliations and vector fields, and energy of maps. Many papers concern special submanifolds in Riemannian and Lorentzian manifolds, such as those with constant mean (scalar, Gauss, etc.) curvature and those with finite total curvature. Contents: Hypersurfaces with Constant Higher Order Mean Curvature in Euclidean Space (L J Alías & J M Malacarne)Uniqueness of Spacelike Hypersurfaces with Constant Mean Curvature in Generalized Robertson–Walker Spacetimes (L J Alías & S Montiel)Critical Points of Willmore–Chen Tension Functionals (M Barros)Some Generalizations of Twistor Spaces (D E Blair)The Intrinsic Torsion of SU(3) and G2 Structures (S Chiossi & S Salamon)H-Hypersurfaces with Finite Total Curvature (M P do Carmo)Volume and Energy of Vector Fields on Spheres. A Survey (O Gil-Medrano)Spacelike Jordan Osserman Algebraic Curvature Tensors in the Higher Signature Setting (P B Gilkey & R Ivanova)The Gauss Map of Minimal Surfaces (A Ros)On Minimal Growth in Group Theory and Riemannian Geometry (A Sambusetti)Deformation of Lipschitz Riemannian Metrics in the Direction of their Ricci Curvature (M Simon)and other papers Readership: Graduate students and researchers in differential geometry. Keywords:
Strings and Geometry by Clay Mathematics Institute. Summer School,Isaac Newton Institute for Mathematical Sciences Pdf
Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.
String-Math 2022 by Ron Donagi,Adrian Langer,Piotr Sułkowski,Katrin Wendland Pdf
This is a proceedings volume from the String-Math conference which took place at the University of Warsaw in 2022. This 12th String-Math conference focused on several research areas actively developing these days. They included generalized (categorical) symmetries in quantum field theory and their relation to topological phases of matter; formal aspects of quantum field theory, in particular twisted holography; various developments in supersymmetric gauge theories, BPS counting and Donaldson–Thomas invariants. Other topics discussed at this conference included new advances in Gromov–Witten theory, curve counting, and Calabi–Yau manifolds. Another broad topic concerned algebraic aspects of conformal field theory, vertex operator algebras, and quantum groups. Furthermore, several other recent developments were presented during the conference, such as understanding the role of operator algebras in the presence of gravity, derivation of gauge-string duality, complexity of black holes, or mathematical aspects of the amplituhedron. This proceedings volume contains articles summarizing 14 conference lectures, devoted to the above topics.
Complex and Symplectic Geometry by Daniele Angella,Costantino Medori,Adriano Tomassini Pdf
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Geometric Flows and the Geometry of Space-time by Vicente Cortés,Klaus Kröncke,Jan Louis Pdf
This book consists of two lecture notes on geometric flow equations (O. Schnürer) and Lorentzian geometry - holonomy, spinors and Cauchy Problems (H. Baum and T. Leistner) written by leading experts in these fields. It grew out of the summer school “Geometric flows and the geometry of space-time” held in Hamburg (2016) and provides an excellent introduction for students of mathematics and theoretical physics to important themes of current research in global analysis, differential geometry and mathematical physics
