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E-raamat: Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses

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  • Formaat: PDF+DRM
  • Sari: Fields Institute Monographs 34
  • Ilmumisaeg: 27-Aug-2015
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781493928309
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  • Formaat: PDF+DRM
  • Sari: Fields Institute Monographs 34
  • Ilmumisaeg: 27-Aug-2015
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781493928309

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This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area.

The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Part I K3 Surfaces: Arithmetic, Geometry and Moduli The Geometry and Moduli of K3 Surfaces
3(80)
Andrew Harder
Alan Thompson
Picard Ranks of K3 Surfaces of BHK Type
45(20)
Tyler L. Kelly
Reflexive Polytopes and Lattice-Polarized K3 Surfaces
65(18)
Ursula Whitcher
Part II Hodge Theory and Transcendental Theory An Introduction to Hodge Structures
83(128)
Sara Angela Filippini
Helge Ruddat
Alan Thompson
Introduction to Nonabelian Hodge Theory
131(42)
Alberto Garcia-Raboso
Steven Rayan
Algebraic and Arithmetic Properties of Period Maps
173(38)
Matt Kerr
Part III Physics of Mirror Symmetry
Mirror Symmetry in Physics: The Basics
211(70)
Callum Quigley
Part IV Enumerative Geometry: Gromov--Witten and Related Invariants
Introduction to Gromov--Witten Theory
281(22)
Simon C.F. Rose
Introduction to Donaldson--Thomas and Stable Pair Invariants
303(12)
Michel van Garrel
Donaldson--Thomas Invariants and Wall-Crossing Formulas
315(22)
Yuecheng Zhu
Part V Gross--Siebert Program
Enumerative Aspects of the Gross--Siebert Program
337(86)
Michel van Garrel
D. Peter Overholser
Helge Ruddat
Part VI Modular Forms in String Theory
Introduction to Modular Forms
423(22)
Simon C.F. Rose
Lectures on BCOV Holomorphic Anomaly Equations
445(30)
Atsushi Kanazawa
Jie Zhou
Polynomial Structure of Topological String Partition Functions
475(28)
Jie Zhou
Part VII Arithmetic Aspects of Calabi--Yau Manifolds
Introduction to Arithmetic Mirror Symmetry
503(38)
Andrija Perunicic
Index 541