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Gentle Introduction to Homological Mirror Symmetry [Kõva köide]

(Universiteit van Amsterdam)
  • Formaat: Hardback, 400 pages, kõrgus x laius x paksus: 235x158x29 mm, kaal: 764 g, Worked examples or Exercises
  • Sari: London Mathematical Society Student Texts
  • Ilmumisaeg: 19-Aug-2021
  • Kirjastus: Cambridge University Press
  • ISBN-10: 110848350X
  • ISBN-13: 9781108483506
Teised raamatud teemal:
Gentle Introduction to Homological Mirror SymmetrySuurem pilt
  • Formaat: Hardback, 400 pages, kõrgus x laius x paksus: 235x158x29 mm, kaal: 764 g, Worked examples or Exercises
  • Sari: London Mathematical Society Student Texts
  • Ilmumisaeg: 19-Aug-2021
  • Kirjastus: Cambridge University Press
  • ISBN-10: 110848350X
  • ISBN-13: 9781108483506
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781108483506.html
Märksõnad:
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.

Originating in mathematical physics, homological mirror symmetry reveals deep connections between different areas of geometry and algebra. This book, which is aimed at graduate students, offers a self-contained and accessible introduction to the subject from the perspective of representation theory of algebras and quivers.

Arvustused

'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

Muu info

Introduction to homological mirror symmetry from the point of view of representation theory, suitable for graduate students.
Part I. To A8 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.