Geometrical Themes Inspired by the N-body Problem
Geometrical Themes Inspired by the N-body Problem

Author: Luis Hernández-Lamoneda

Publisher: Springer

Published: 2018-02-26

Total Pages: 133

ISBN-13: 3319714287

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Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order to motivate the McGehee transformation. A. Pedroza’s notes provide a brief introduction to Lagrangian Floer homology and its relation to the solution of the Arnol’d conjecture on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism.

String-Math 2022
String-Math 2022

Author: Ron Donagi

Publisher: American Mathematical Society

Published: 2024-04-18

Total Pages: 306

ISBN-13: 1470472406

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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.

Mathematische Werke / Mathematical Works
Mathematische Werke / Mathematical Works

Author: Erich Kähler

Publisher: Walter de Gruyter

Published: 2011-07-13

Total Pages: 984

ISBN-13: 3110905434

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For most mathematicians and many mathematical physicists the name Erich Kähler is strongly tied to important geometric notions such as Kähler metrics, Kähler manifolds and Kähler groups. They all go back to a paper of 14 pages written in 1932. This, however, is just a small part of Kähler's many outstanding achievements which cover an unusually wide area: From celestial mechanics he got into complex function theory, differential equations, analytic and complex geometry with differential forms, and then into his main topic, i.e. arithmetic geometry where he constructed a system of notions which is a precursor and, in large parts, equivalent to the now used system of Grothendieck and Dieudonné. His principal interest was in finding the unity in the variety of mathematical themes and establishing thus mathematics as a universal language. In this volume Kähler's mathematical papers are collected following a "Tribute to Herrn Erich Kähler" by S. S. Chern, an overview of Kähler's life data by A. Bohm and R. Berndt, and a Survey of his Mathematical Work by the editors. There are also comments and reports on the developments of the main topics of Kähler's work, starting by W. Neumann's paper on the topology of hypersurface singularities, J.-P. Bourguignon's report on Kähler geometry and, among others by Berndt, Bost, Deitmar, Ekeland, Kunz and Krieg, up to A. Nicolai's essay "Supersymmetry, Kähler geometry and Beyond". As Kähler's interest went beyond the realm of mathematics and mathematical physics, any picture of his work would be incomplete without touching his work reaching into other regions. So a short appendix reproduces three of his articles concerning his vision of mathematics as a universal Theme together with an essay by K. Maurin giving an "Approach to the philosophy of Erich Kähler".

The N-Vortex Problem
The N-Vortex Problem

Author: Paul K. Newton

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 430

ISBN-13: 146849290X

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This text is an introduction to current research on the N- vortex problem of fluid mechanics. It describes the Hamiltonian aspects of vortex dynamics as an entry point into the rather large literature on the topic, with exercises at the end of each chapter.

Bulletin of the Atomic Scientists
Bulletin of the Atomic Scientists

Author:

Publisher:

Published: 1959-02

Total Pages: 48

ISBN-13:

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The Bulletin of the Atomic Scientists is the premier public resource on scientific and technological developments that impact global security. Founded by Manhattan Project Scientists, the Bulletin's iconic "Doomsday Clock" stimulates solutions for a safer world.

Restless Reason and Other Variations on Kantian Themes
Restless Reason and Other Variations on Kantian Themes

Author: Amihud Gilead

Publisher: Springer Nature

Published: 2021-11-23

Total Pages: 150

ISBN-13: 3030841979

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This book, combining integratively-revised previously-published papers with entirely new chapters, challenges and treats some major problems in Kant’s philosophy not by means of new interpretations but by suggesting some variations on Kantian themes. Such variations are, in fact, reconstructions made according to Kantian ideas and principles and yet cannot be extracted as such directly from his writings. The book also analyses Kant's philosophy from a new metaphysical angle, based on the original metaphysics of the author, called panenmentalism. It reconstructs some missing links in Kant's philosophy, such as the idea of teleological time, which is vital for Kant's moral theory. Although these variations cannot be found literally in Kant’s works, they can be legitimately explicated, developed, and implied from them. Such is the case because these variations are strictly compatible with the details of the texts and the texts as wholes, and because they are systematically integrated. Their coherence supports their validation. The target audiences are graduate and PhD students as well as specialist researchers of Kant's philosophy.

Dynamical Systems
Dynamical Systems

Author: Wang Sang Koon

Publisher: Springer

Published: 2011-06-01

Total Pages: 336

ISBN-13: 9780387495156

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This book considers global solutions to the restricted three-body problem from a geometric point of view. The authors seek dynamical channels in the phase space which wind around the planets and moons and naturally connect them. These low energy passageways could slash the amount of fuel spacecraft need to explore and develop our solar system. In order to effectively exploit these passageways, the book addresses the global transport. It goes beyond the traditional scope of libration point mission design, developing tools for the design of trajectories which take full advantage of natural three or more body dynamics, thereby saving precious fuel and gaining flexibility in mission planning. This is the key for the development of some NASA mission trajectories, such as low energy libration point orbit missions (e.g., the sample return Genesis Discovery Mission), low energy lunar missions and low energy tours of outer planet moon systems, such as a mission to tour and explore in detail the icy moons of Jupiter. This book can serve as a valuable resource for graduate students and advanced undergraduates in applied mathematics and aerospace engineering, as well as a manual for practitioners who work on libration point and deep space missions in industry and at government laboratories. the authors include a wealth of background material, but also bring the reader up to a portion of the research frontier.