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Homological Mirror Symmetry: New Developments and Perspectives 2009 ed. [Hardback]

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  • Formāts: Hardback, 272 pages, height x width: 235x155 mm, weight: 1280 g, XI, 272 p., 1 Hardback
  • Sērija : Lecture Notes in Physics 757
  • Izdošanas datums: 27-Oct-2008
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540680292
  • ISBN-13: 9783540680291
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Homological Mirror Symmetry: New Developments and Perspectives 2009 ed.Palielināt
  • Formāts: Hardback, 272 pages, height x width: 235x155 mm, weight: 1280 g, XI, 272 p., 1 Hardback
  • Sērija : Lecture Notes in Physics 757
  • Izdošanas datums: 27-Oct-2008
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540680292
  • ISBN-13: 9783540680291
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783540680291.html
Keywords:
Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap in the literature by providing a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A. Kapustin, L. Katzarkov, A. Klemm, M. Kontsevich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematical aspects of quantum field theory.
The Symplectic Geometry of Cotangent Bundles from a Categorical Viewpoint
K. Fukaya, P. Seidel, and I. Smith
1
1 Overview
1
2 Constructible Sheaves
6
3 Lefschetz Thimbles
11
4 Family Floer Cohomology
15
5 The Non-simply-Connected Case
22
References
25
B-Type D-Branes in Toric Calabi-Yau Varieties
M. Herbst, K. Hori, and D. Page
27
1 Introduction
27
2 D-branes in the Linear Sigma Model
31
3 D-Branes on Toric Varieties
33
4 Changing the Phase — The Grade Restriction Rule
36
5 Some Relations to Earlier Work
41
References
43
Topological String Theory on Compact Calabi-Yau: Modularity and Boundary Conditions
M.-x. Huang, A. Klemm, and S. Quackenbush
45
1 Outline
45
2 The Topological B-Model
48
3 Quintic
55
4 One-Parameter Calabi-Yau Spaces with Three Regular Singular Points
69
5 Symplectic Invariants at Large Radius
77
6 Conclusions
88
A Appendices
93
References
99
Gauge Theory, Mirror Symmetry, and the Geometric Langlands Program
A. Kapustin
103
1 Introduction
103
2 Montonen–Olive Duality
104
3 Twisting N = 4 Super-Yang-Mills Theory
107
4 Reduction to Two Dimensions
110
5 Mirror Symmetry for the Hitchin Moduli Space
113
6 From A-Branes to D-Modules
115
7 Wilson and 't Hooft Operators
119
References
122
Homological Mirror Symmetry and Algebraic Cycles
L. Katzarkov
125
1 Introduction
125
2 Definitions
126
3 The Construction
130
4 Birational Transformations and HMS
132
5 Studying Non-rationality
138
6 Non-rationality of Generic four Dimensional Cubic
142
7 Homological Mirror Symmetry and Algebraic Cycles
147
References
150
Notes on Ainfinity-Algebras, Ainfinity-Categories and Non-Commutative Geometry
M. Kontsevich and Y. Soibelman
153
1 Introduction
153
2 Coalgebras and Non-commutative Schemes
158
3 Ainfinity-Algebras
165
4 Non-Commutative dg-line L and Weak Unit
169
5 Modules and Bimodules
171
6 Yoneda Lemma
174
7 Hochschild Cochain and Chain Complexes of an Ainfinity-Algebra
175
8 Homologically Smooth and Compact Ainfinity-Algebras
183
9 Degeneration Hodge-to-de Rham
186
10 Ainfinity-Algebras with Scalar Product
189
11 Hochschild Complexes as Algebras Over Operads and PROPs
194
12 Appendix
213
References
218
On Non-Commutative Analytic Spaces Over NonArchimedean Fields
Y. Soibelman
221
1 Introduction
221
2 Non-Commutative Berkovich Spectrum
227
3 Non-Commutative Affinoid Algebras
231
4 Non-Commutative Analytic Affine Spaces
232
5 Quantum Analytic Tori
233
6 Non-Commutative Stein Spaces
236
7 Non-Commutative Analytic K3 Surfaces
237
References
246
Derived Categories and Stacks in Physics
E. Sharpe
249
1 Introduction
249
2 The Renormalization Group
250
3 Derived Categories in Physics
251
4 Stacks in Physics
258
5 Conclusions
270
References
270