Symplectic geometry and mirror symmetry: proceedings of the 4th KIAS Annual International Conference, Korea Institute for Advanced Study, Seoul, South Korea, 14-18 August 2000

Speakers......Page 6
Preface......Page 8
Contents......Page 10
1 Introduction......Page 12
2 Ample bundles over almost-complex manifolds......Page 13
3 Estimated transversality in jet bundles......Page 18
4 Proof of the main result......Page 25
5 Examples and applications......Page 32
References......Page 40
1 Introduction......Page 42
2 SU(2) Gauge Theory without Matter......Page 43
3 Small and Large Radius Limits......Page 48
4 SU(2) theory with matter......Page 49
5 Discussions......Page 53
References......Page 59
The Toda conjecture......Page 62
1 Witten's conjecture......Page 63
2 The Toda lattice......Page 68
3 Hamiltonian operators and the Toda lattice......Page 73
4 The Toda conjecture......Page 77
5 The Toda conjecture and the Virasoro conjecture......Page 81
6 Propagating the Toda conjecture......Page 87
References......Page 88
Introduction......Page 92
1 The Basic Construction......Page 93
2 Resolutions of Toric Singularities......Page 96
3 Deformations of toric singularities......Page 104
4 Local mirror symmetry and connections with the work of Ruan and Joyce......Page 109
5 The Future of the SYZ Conjecture......Page 115
References......Page 119
1 Introduction......Page 122
2 N - 2 Boundary Superspace......Page 125
3 A Linear Model: An Example......Page 132
4 A-Type D-Branes in Linear Sigma Model......Page 142
5 B-type D-Branes and Tachyom Condensation......Page 160
6 B-Type D-Branes in Landau-Ginzburg Model......Page 179
Acknowledgement......Page 191
References......Page 192
0 Introduction......Page 198
1 The torus action on G/P......Page 200
2 The C*-fiow......Page 203
3 Connectedness......Page 205
4 Rationality......Page 208
References......Page 211
1 Introduction......Page 214
2 Degenerations of unitary Conformal Field Theories......Page 217
3 Calabi-Yau manifolds in the large complex structure limit......Page 225
4 Aoo-algebras and Aoo-categories......Page 233
5 Fukaya category and its degeneration......Page 239
6 Morse-Smale complex and the category of Morse functions......Page 246
7 Aoo-structure for the derived category of coherent sheaves......Page 258
8 Homological mirror conjecture......Page 261
9 Appendix: constructions in the case of complex numbers......Page 267
References......Page 271
Genus-1 Virasoro conjecture on the small phase space......Page 276
1 Genus-1 Virasoro conjecture on the small phase space......Page 277
2 Compatibility of functions ok......Page 280
3 Some sufficient conditions for genus-1 Virasoro conjecture......Page 284
References......Page 289
Obstruction to and deformation of Lagrangian intersection Floer cohomology......Page 292
1. Preliminaries and problems to overcome......Page 293
2. Orientations and obstruction classes......Page 297
3. Construction of the obstruction classes......Page 300
4. Aoo-deformation of Lagrangian submanifold......Page 303
5. Bounding cochains and deformation......Page 312
6. Some applications......Page 318
References......Page 320
1 Introduction......Page 322
2 Preliminary......Page 334
3 Topological Open Membrane......Page 353
4 Back to the strings......Page 375
References......Page 389
1 Introduction......Page 396
2 Quintic case......Page 401
3 The mirror of quintic......Page 408
4 Calabi-Yau hyper surfaces and complete Intersections in toric variety......Page 413
5 Conifold transition......Page 416
6 Calabi-Yau complete Intersection In flag manifold......Page 427
References......Page 436
1. INTRODUCTION......Page 440
2. BRANCHED COVERS......Page 442
3. EXAMPLES FROM ALGEBRAIC GEOMETRY......Page 447
4. FLOER COHOMOLOGY FOR AUTOMORPHISMS......Page 453
5. HOCHSCHILD COHOMOLOGY......Page 457
6. HOCHSCHILD COHOMOLOGY AND GLOBAL MONODROMY......Page 459
7. MORSE CATEGORIES......Page 465
8. REAL STRUCTURES......Page 468
9. MATCHING PAIRS AND MATCHING PATHS......Page 470
REFERENCES......Page 475
1 Introduction......Page 478
2 Chern-Simons-type functionals and critical points......Page 481
3 Gauge equivalence and moment maps......Page 485
4 Relationship to Kontsevich's mirror conjecture......Page 500
5 Stability......Page 503
6 The 2-torus......Page 504
References......Page 506