Foundations of mathematics and physics one century after Hilbert : new perspectives /: new perspectives. (2018)

• Record Type: Book
• Further Information: Note: Joseph Kouneiher, editor.
• Editors: Kouneiher, Joseph
• Contents: Intro; Preface; Mathematics and Physics: A Common Matter?; Truth, Depth, and Beauty; References; Acknowledgements; Contents; Summary; Where We Stand Today; 1 Hilbert and the Foundations of Mathematics and Physics; 2 The Rise of Mathematical-Physics; 3 Gauges Theories, Dualities and Fiber bundles; 3.1 Connections in a Fiber Bundle (Elie Cartan); 3.2 The Dawn of Mathematical Physics; 3.3 Algebraic Geometry, Cohomology and Strings theories; 3.4 Cohomology and Invariants; 3.5 String Theory; 3.6 Loop Quantum Gravity; 3.7 Connections Versus Holonomies; 3.8 Quantisation; 4 Non-commutative Geometry 4.1 Preliminaries5 Twistor Theory; 5.1 Renormalization and Hilbert's Twenty-First Problem; 5.2 Renormalisation; 5.3 Feynman Diagrams and Perturbative Renomalization; 5.4 Connes-Kreimer's Approach; 6 Dualities, QFT and Integrable Systems; 6.1 Matter; 6.2 Solitons, Dualities and Integrable Systems; 6.3 The Sine-Gordon Equation; 7 Symmetry and the Foundations of Physics; 8 The Modern Cosmology; 9 Einstein's Fields Equations -- EFE; 9.1 Solutions of EFE and the Standard Model of Cosmology; 9.2 Friedmann Equation; 9.3 Hubble Expansion 10 Friedmann-Robertson-Walker (FRW) Cyclic Universe and Elliptic Curves11 Conclusion; References; Mie's Electromagnetic Theory of Matter and the Background to Hilbert's Unified Foundations of Physics; 1 Introduction; 2 Gustav Mie's Electromagnetic Theory of Matter; 3 Contemporary Debates on Gravitation; 4 Born's Formulation of Mie's Theory; 5 Hilbert's Communication and Mie's Theory; 6 Concluding Remarks; References; Hilbert and Einstein; 1 Introduction; 2 The Encounter That Never Took Place (1912); 3 The Fateful Encounter (1915-1916):; 4 The Tragic-Comic Encounte-(1928-29): 5 L'envoi (1932):References; Grothendieck's Unifying Vision of Geometry; 1 Pictorial Visualization I: Schemes and Crystals; 2 This Geometry Before Grothendieck; 2.1 Genus; 2.2 Counting Solutions Without Finding Them; 2.3 Local and Global; 3 Cohomology in Grothendieck's Words; 3.1 Pictorial Visualization II: Compass Drawings; 3.2 The Sea Rises Around Cohomology; 4 The Spectacular Flight of the New Geometry; 4.1 The Proper Object of Topology; 4.2 The Long Awaited Marriage of Geometry and Arithmetic; 5 Logical Foundations and Mathematical Progress; References Understanding the 6-Dimensional Sphere1 Introduction; 2 Relativistic Physics; 3 Finite Symmetries; 4 Proof of the Theorem; 5 Future Generalization; References; A Dozen Problems, Questions and Conjectures About Positive Scalar Curvature; 1 Definition of Scalar Curvature; 2 Soft and Hard Facets of Scalar Curvature; 3 Bounds on the Uryson Width, Slicing Area and Filling Radius; 4 Extremality and Rigidity with Positive Scalar Curvature; 5 Extremality and Gap Extremality of Open Manifolds.; 6 Bounds on Widths of Bands with Positive Curvatures; 7 Extremality and Rigidity of Convex Polyhedra
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 530.09; Mathematics; Physics -- History; Mathematics -- History; SCIENCE / Energy; SCIENCE / Mechanics / General; SCIENCE / Physics / General; Mathematics; Physics; Science -- Mathematical Physics; Science -- Physics; Mathematics -- History & Philosophy; Mathematical physics; History of science; History of mathematics; Electronic books; History
• Languages: English
• ISBNs: 9783319648132; 3319648136
• Related ISBNs: 9783319648125; 3319648128
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed June 1, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.