| 1 |
The origins of mirror symmetry; overview of the course |
(PDF) |
| 2 |
Deformations of complex structures |
(PDF) |
| 3 |
Deformations continued, Hodge theory; pseudoholomorphic curves, transversality |
(PDF) |
| 4 |
Pseudoholomorphic curves, compactness, Gromov-Witten invariants |
(PDF) |
| 5 |
Quantum cohomology and Yukawa coupling on H1,1; Kähler moduli space |
(PDF) |
| 6 |
The quintic 3-fold and its mirror; complex degenerations and monodromy |
(PDF) |
| 7 |
Monodromy weight filtration, large complex structure limit, canonical coordinates |
(PDF) |
| 8 |
Canonical coordinates and mirror symmetry; the holomorphic volume form on the mirror quintic and its periods |
(PDF) |
| 9 |
Picard-Fuchs equation and canonical coordinates for the quintic mirror family |
(PDF) |
| 10 |
Yukawa couplings and numbers of rational curves on the quintic; introduction to homological mirror symmetry |
(PDF) |
| 11 |
Lagrangian Floer homology |
(PDF) |
| 12 |
Lagrangian Floer theory: Hamiltonian isotopy invariance, grading, examples |
(PDF) |
| 13 |
Lagrangian Floer theory: product structures, A_∞ equations |
(PDF) |
| 14 |
Fukaya categories: first version; Floer homology twisted by flat bundles; defining CF(L,L) |
(PDF) |
| 15 |
Defining CF(L,L) continued; discs and obstruction. Coherent sheaves, examples, introduction to ext. |
(PDF) |
| 16 |
Ext groups; motivation for the derived category |
(PDF) |
| 17 |
The derived category; exact triangles; homs and exts. |
(PDF) |
| 18 |
Twisted complexes and the derived Fukaya category; Dehn twists, connected sums and exact triangles |
(PDF) |
| 19 |
Homological mirror symmetry: the elliptic curve; theta functions and Floer products |
(PDF) |
| 20 |
HMS for the elliptic curve: Massey products; motivation for the SYZ conjecture |
(PDF) |
| 21 |
The SYZ conjecture; special Lagrangian submanifolds and their deformations |
(PDF) |
| 22 |
The moduli space of special Lagrangians: affine structures; mirror complex structure and Kähler form |
(PDF) |
| 23 |
SYZ continued; examples: elliptic curves, K3 surfaces |
(PDF) |
| 24 |
SYZ from toric degenerations (K3 case); Landau-Ginzburg models, superpotentials; example: the mirror of CP1 |
(PDF) |
| 25 |
Homological mirror symmetry for CP1: matrix factorizations, admissible Lagrangians, etc. |
(PDF) |
