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.
Bibliographic references
Includes bibliographical references and index.
Contents
The Geometry and Moduli of K3 Surfaces / Andrew Harder, Alan Thompson)
Picard Ranks of K3 Surfaces of BHK Type / Tyler L. Kelly
Reflexive Polytopes and Lattice-Polarized K3 Surfaces / Ursula Whitcher
An Introduction to Hodge Theory / Sara A. Filippini, Helge Ruddat, Alan Thompson
Introduction to Nonabelian Hodge Theory / Alberto Garcia-Raboso, Steven Rayan
Algebraic and Arithmetic Properties of Period Maps / Matt Kerr
Mirror Symmetry in Physics / Callum Quigley
Introduction to Gromov–Witten Theory / Simon C. F. Rose
Introduction to Donaldson–Thomas and Stable Pair Invariants / Michel van Garrel
Donaldson–Thomas Invariants and Wall-Crossing Formulas / Yuecheng Zhu
Enumerative Aspects of the Gross–Siebert Program / Michel van Garrel, D. Peter Overholser, Helge Ruddat
Introduction to Modular Forms / Simon C. F. Rose
Lectures on Holomorphic Anomaly Equations / Atsushi Kanazawa, Jie Zhou
Polynomial Structure of Topological Partition Functions Jie Zhou
Introduction to Arithmetic Mirror Symmetry / Andrija Peruničić.
ISBN
9781493928293 ((hbk.))
1493928295 ((hbk.))
LCCN
2015945196
OCLC
921827572
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