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Book
Tropical and Logarithmic Methods in Enumerative Geometry
Authors: --- ---
ISBN: 3031394011 3031394003 Year: 2023 Publisher: Cham, Switzerland : Birkhäuser,

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Abstract

This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.

Enumerative geometry and string theory.
Author:
ISBN: 0821836870 9780821836873 Year: 2006 Volume: 32 Publisher: Providence (R.I.) American Mathematical Society


Book
Curvilinear micromagnetism : from fundamentals to applications
Authors: ---
ISBN: 3031090853 3031090861 Year: 2022 Publisher: Cham, Switzerland : Springer,

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Curves and singularities : A geometrical introduction to singularity theory.
Authors: ---
ISBN: 0521429994 0521419859 9780521429993 9780521419857 9781139172615 Year: 1992 Publisher: Cambridge : Cambridge University Press,


Book
Enumerative invariants in algebraic geometry and string theory : lectures given at the C. I. M. E. summer school held in Cetraro, Italy, June 6-11 2005
Authors: ---
ISBN: 3540798145 3540798137 Year: 2008 Publisher: Berlin ; Heidelberg : Springer-Verlag,

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Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.

Differential geometry of curves and surfaces
Author:
ISBN: 0132125897 9780132125895 Year: 1976 Publisher: Englewood Cliffs, NJ : Prentice-Hall,


Book
Géométrie des courbes et des surfaces
Authors: ---
ISBN: 2705658416 9782705658410 Year: 1976 Publisher: Paris Hermann


Book
Hypersonic curved compression inlet and its inverse design
Author:
ISBN: 9811507279 9811507260 Year: 2020 Publisher: Singapore : Springer Singapore : Imprint: Springer,

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This book presents systematic research results on curved shock wave-curved compression surface applied to the compression surface design of supersonic–hypersonic inlet, which is a brand new inlet design. The concept of supersonic inlet curved compression discussed originated from the author’s research at the Deutsches Zentrum fur Luft- und Raumfahrt (DLR SM-ES) in the early 1990s. This book introduces the research history, working characteristics, performance calculation and aerodynamic configuration design method of this compression mode in detail. It also describes method of estimating the minimum drag in inlet and drag reduction effect of curved compression and proposes a new index for evaluating unit area compression efficiency of the inlet. Further, it reviews the relevant recent research on curved compression. As such it is a valuable resource for students, researchers and scientists in the fields of hypersonic propulsion and aeronautics.


Book
Infinite Dimensional Algebras and Quantum Integrable Systems
Authors: --- --- ---
ISBN: 1280459581 9786610459582 3764373415 Year: 2005 Volume: 237 Publisher: Basel : Birkhäuser Basel : Imprint: Birkhäuser,

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This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems'' held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV. International Congress on Mathematical Physics. Recent developments in the theory of infinite dimensional algebras and their applications to quantum integrable systems are reviewed by some of the leading experts in the field. The volume will be of interest to a broad audience from graduate students to researchers in mathematical physics and related fields. Contributors: E. Frenkel O.A. Castro-Alvaredo and A. Fring V.G. Kac and M. Wakimoto A. Gerasimov, S. Kharchev and D. Lebedev H.E. Boos, V.E. Korepin and F.A. Smirnov Kanehisa Takasaki Takashi Takebe L.A. Takhtajan and Lee-Peng Teo V. Tarasov.


Book
An Invitation to Quantum Cohomology : Kontsevich's Formula for Rational Plane Curves
Authors: ---
ISBN: 0817644954 Year: 2007 Volume: 249 Publisher: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser,

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This book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint is mostly that of enumerative geometry, and the red thread of the exposition is the problem of counting rational plane curves. Kontsevich's formula is initially established in the framework of classical enumerative geometry, then as a statement about reconstruction for Gromov–Witten invariants, and finally, using generating functions, as a special case of the associativity of the quantum product. Emphasis is given throughout the exposition to examples, heuristic discussions, and simple applications of the basic tools to best convey the intuition behind the subject. The book demystifies these new quantum techniques by showing how they fit into classical algebraic geometry. Some familiarity with basic algebraic geometry and elementary intersection theory is assumed. Each chapter concludes with some historical comments and an outline of key topics and themes as a guide for further study, followed by a collection of exercises that complement the material covered and reinforce computational skills. As such, the book is ideal for self-study, as a text for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory. The book will prove equally useful to graduate students in the classroom setting as to researchers in geometry and physics who wish to learn about the subject.

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