Lecture Notes · Lecture Notes
MIT OpenCourseWare
Topics in Geometry: Mirror Symmetry
Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain
- Instructor
- Prof. Denis Auroux
- Term
- Spring 2009
- Level
- Graduate
- What's inside
- 1 lecture note · 1 reading · 25 other files · 1 web page
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.969 Topics in Geometry: Mirror Symmetry, Spring 2009, Prof. Denis Auroux — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- A lecture sequence of 25 items is confirmed. No assignments or exams were found for this course, so it stays as organized materials rather than a full course order.
Not included here
5 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (5 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Notes
25 files
- Mirror Symmetry: Lecture 2 Download
- Mirror Symmetry: Lecture 2 Download
- Mirror Symmetry: Lecture 3 Download
- Mirror Symmetry: Lecture 4 Download
- Mirror Symmetry: Lecture 5 Download
- Mirror Symmetry: Lecture 6 Download
- Mirror Symmetry: Lecture 7 Download
- Mirror Symmetry: Lecture 8 Download
- Mirror Symmetry: Lecture 10 Download
- Mirror Symmetry: Lecture 11 Download
- Mirror Symmetry: Lecture 11 Download
- Mirror Symmetry: Lecture 12 Download
- Mirror Symmetry: Lecture 13 Download
- Mirror Symmetry: Lecture 14 Download
- Mirror Symmetry: Lecture 15 Download
- Mirror Symmetry: Lecture 16 Download
- Mirror Symmetry: Lecture 17 Download
- Mirror Symmetry: Lecture 18 Download
- Mirror Symmetry: Lecture 19 Download
- Mirror Symmetry: Lecture 20 Download
- Mirror Symmetry: Lecture 21 Download
- Mirror Symmetry: Lecture 22 Download
- Mirror Symmetry: Lecture 23 Download
- Mirror Symmetry: Lecture 24 Download
- Mirror Symmetry: Lecture 25 Download
Course outline
Lecture Notes · Lecture Notes
Lecture 2: Deformations of complex structures
Lecture Notes · Lecture Notes
Lecture 3: Deformations continued, Hodge theory; pseudoholomorphic curves, transversality
Lecture Notes · Lecture Notes
Lecture 4: Pseudoholomorphic curves, compactness, Gromov-Witten invariants
Lecture Notes · Lecture Notes
Lecture 5: Quantum cohomology and Yukawa coupling on H¹,¹; Kähler moduli space
Lecture Notes · Lecture Notes
Lecture 6: The quintic 3-fold and its mirror; complex degenerations and monodromy
Lecture Notes · Lecture Notes
Lecture 7: Monodromy weight filtration, large complex structure limit, canonical coordinates
Lecture Notes · Lecture Notes
Lecture 8: Canonical coordinates and mirror symmetry; the holomorphic volume form on the mirror quintic and its periods
Lecture Notes · Lecture Notes
Lecture 9: Picard-Fuchs equation and canonical coordinates for the quintic mirror family
Lecture Notes · Lecture Notes
Lecture 10: Yukawa couplings and numbers of rational curves on the quintic; introduction to homological mirror symmetry
Lecture Notes · Lecture Notes
Lecture 11: Lagrangian Floer homology
Lecture Notes · Lecture Notes
Lecture 12: Lagrangian Floer theory: Hamiltonian isotopy invariance, grading, examples
Lecture Notes · Lecture Notes
Lecture 13: Lagrangian Floer theory: product structures, A_∞ equations
Lecture Notes · Lecture Notes
Lecture 14: Fukaya categories: first version; Floer homology twisted by flat bundles; defining CF(L,L)
Lecture Notes · Lecture Notes
Lecture 15: Defining CF(L,L) continued; discs and obstruction. Coherent sheaves, examples, introduction to ext.
Lecture Notes · Lecture Notes
Lecture 16: Ext groups; motivation for the derived category
Lecture Notes · Lecture Notes
Lecture 17: The derived category; exact triangles; homs and exts.
Lecture Notes · Lecture Notes
Lecture 18: Twisted complexes and the derived Fukaya category; Dehn twists, connected sums and exact triangles
Lecture Notes · Lecture Notes
Lecture 19: Homological mirror symmetry: the elliptic curve; theta functions and Floer products
Lecture Notes · Lecture Notes
Lecture 20: HMS for the elliptic curve: Massey products; motivation for the SYZ conjecture
Lecture Notes · Lecture Notes
Lecture 21: The SYZ conjecture; special Lagrangian submanifolds and their deformations
Lecture Notes · Lecture Notes
Lecture 22: The moduli space of special Lagrangians: affine structures; mirror complex structure and Kähler form
Lecture Notes · Lecture Notes
Lecture 23: SYZ continued; examples: elliptic curves, K3 surfaces
Lecture Notes · Lecture Notes
Lecture 24: SYZ from toric degenerations (K3 case); Landau-Ginzburg models, superpotentials; example: the mirror of CP¹
Lecture Notes · Lecture Notes
Lecture 25: Homological mirror symmetry for CP¹: matrix factorizations, admissible Lagrangians, etc.
MIT OpenCourseWare, Prof. Denis Auroux, 18.969 Topics in Geometry: Mirror Symmetry, Spring 2009.
License: CC BY-NC-SA 4.0 · Edition: Spring 2009 · Open the original course on OCW ↗
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