Gentle Introduction to Homological Mirror Symmetry

Homological mirror symmetry is a mathematical concept that connects geometry and algebra, revealing deep connections between different areas of mathematics. This book provides a self-contained introduction to the subject through the representation theory of algebras and quivers, making it accessible to graduate students and others without a deep background in homological algebra and modern geometry.

\n Format: Paperback / softback
\n Length: 400 pages
\n Publication date: 19 August 2021
\n Publisher: Cambridge University Press
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Homological mirror symmetry, a fascinating concept that originated in theoretical physics, has gained significant attention in mathematics due to its profound connections between various branches of geometry and algebra. This comprehensive book provides a self-contained and accessible introduction to the subject, utilizing the representation theory of algebras and quivers. It is particularly suitable for graduate students and individuals with limited background in homological algebra and modern geometry.

The book is organized into three parts, each offering a distinct perspective on homological mirror symmetry. Part I delves into the A-infinity formalism, providing a glimpse of mirror symmetry through representations of quivers. Part II explores various A- and B-models in mirror symmetry, highlighting their connections through toric and tropical geometry. Part III focuses on mirror symmetry for Riemann surfaces, presenting the main mathematical ideas through concise examples derived mainly from the theory of surfaces. These examples serve as a valuable tool for bridging theory and intuition, aiding the reader in grasping the intricacies of homological mirror symmetry.

By presenting the material in a clear and concise manner, this book serves as an invaluable resource for scholars and researchers seeking to explore the rich interplay between geometry and algebra in the context of homological mirror symmetry. Whether you are a student, professional, or simply interested in the mathematical world, this book will provide you with a solid foundation to understand and appreciate this fascinating field.

\n Weight: 620g\n
Dimension: 152 x 230 x 32 (mm)\n
ISBN-13: 9781108728751\n \n