A Gentle Introduction to Homological Mirror Symmetry

Raf Bocklandt (Universiteit van Amsterdam)

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English

Cambridge University Press
19 August 2021

Algebra; Algebraic geometry; Algebraic topology; Quantum physics (quantum mechanics & quantum field theory); Mathematical physics

Series: London Mathematical Society Student Texts

Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Part I introduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various A- and B-models in mirror symmetry and their connections through toric and tropical geometry. Part III deals with mirror symmetry for Riemann surfaces. The main mathematical ideas are illustrated by means of simple examples coming mainly from the theory of surfaces, helping the reader connect theory with intuition.

By: Raf Bocklandt (Universiteit van Amsterdam)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 228mm, Width: 150mm, Spine: 25mm
Weight: 628g
ISBN: 9781108728751
ISBN 10: 1108728758
Series: London Mathematical Society Student Texts
Pages: 400
Publication Date: 19 August 2021
Audience: Professional and scholarly , College/higher education , Undergraduate , Primary
Format: Paperback
Publisher's Status: Active

Part I. To A∞ and Beyond: 1. Categories; 2. Cohomology; 3. Higher products; 4. Quivers; Part II. A Glance through the Mirror: 5. Motivation from physics; 6. The A-side; 7. The B-side; 8. Mirror symmetry; Part III. Reflections on Surfaces: 9. Gluing; 10. Grading; 11. Stabilizing; 12. Deforming; References; Index.

Raf Bocklandt is Lecturer in Mathematics at the University of Amsterdam.

Reviews for A Gentle Introduction to Homological Mirror Symmetry

'Each chapter concludes with a few exercises, and great care has been taken to use notation and terminology in a consistent way. That must have taken considerable effort and it greatly increases the value of the book because there are many examples in mirror symmetry of different writers using the same words to mean different, often subtly different, things.' G. K. Sankaran, MathSciNet 'The book under review provides an introduction to homological mirror symmetry which is accessible to graduate students in mathematics. In particular, it includes a great amount of background material, and motivational sections. Among the reason it is so approachable is the style …' Hulya Arguz, zbMATH