Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Lecture Notes on Concentrated Graduate Courses

  • Radu Laza
  • Matthias Schütt
  • Noriko Yui

Part of the Fields Institute Monographs book series (FIM, volume 34)

Table of contents

  1. Front Matter
    Pages i-x
  2. K3 Surfaces: Arithmetic, Geometry and Moduli

    1. Front Matter
      Pages 1-1
    2. Andrew Harder, Alan Thompson
      Pages 3-43
    3. Tyler L. Kelly
      Pages 45-63
  3. Hodge Theory and Transcendental Theory

    1. Front Matter
      Pages 81-81
    2. Sara Angela Filippini, Helge Ruddat, Alan Thompson
      Pages 83-130
    3. Alberto García-Raboso, Steven Rayan
      Pages 131-171
  4. Physics of Mirror Symmetry

    1. Front Matter
      Pages 209-209
    2. Callum Quigley
      Pages 211-278
  5. Enumerative Geometry: Gromov–Witten and Related Invariants

    1. Front Matter
      Pages 279-279
    2. Simon C. F. Rose
      Pages 281-301
  6. Gross–Siebert Program

    1. Front Matter
      Pages 335-335
    2. Michel van Garrel, D. Peter Overholser, Helge Ruddat
      Pages 337-420
  7. Modular Forms in String Theory

    1. Front Matter
      Pages 421-421
    2. Simon C. F. Rose
      Pages 423-444
    3. Atsushi Kanazawa, Jie Zhou
      Pages 445-473
  8. Arithmetic Aspects of Calabi–Yau Manifolds

    1. Front Matter
      Pages 501-501
    2. Andrija Peruničić
      Pages 503-539
  9. Back Matter
    Pages 541-547

About this book


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.


Donaldson–Thomas invariants Gromov–Witten theory Gross–Siebert program Hodge theory mirror symmetry moduli problem string theory toric approach

Editors and affiliations

  • Radu Laza
    • 1
  • Matthias Schütt
    • 2
  • Noriko Yui
    • 3
  1. 1.Mathematics DepartmentStony Brook UniversityStony BrookUSA
  2. 2.Leibniz Universität HannoverHannoverGermany
  3. 3.Department of Math & StatsQueen's UniversityKingstonCanada

Bibliographic information