Math
226B: Fukaya CategoriesFall 2023 Syllabus Fukaya categories occupy a central role in modern mathematics, at the junction of algebraic geometry, symplectic geometry, low-dimensional topology, and mathematical physics. The goal of this course is to give an introduction to Lagrangian Floer homology, Fukaya categories, and homological mirror symmetry. Instructor: Ko HondaOffice Hours: Mondays 2:30-3:30pm or by appointmentE-mail: honda at math dot ucla dot eduURL: http://www.math.ucla.edu/~hondaClass Meetings: Lectures are MWF 10-10:50am at MS
5203.Topics- Some symplectic geometry
- Lagrangian Floer (co-)homology
- A-infinity algebras and A-infinity categories
- Construction of the Fukaya categories and some variants including the wrapped Fukaya category
- Exact triangles, twists, split generation
- Homological mirror symmetry e.g. of the torus
Prerequisites:
Math 225 sequence or equivalent (a good knowledge of
differentiable manifolds and homology). Some knowledge of
symplectic geometry is helpful, but not necessary. Grading: TBAReferencesBasics of symplectic geometry: - D. McDuff and D. Salamon, Introduction to symplectic topology, 2nd edition, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1998.
- A.
Cannas da Silva, Lectures
on symplectic geometry.
Fukaya categories: - D. Auroux, A beginner's introduction to Fukaya categories.
- P. Seidel, Fukaya categories and Picard-Lefschetz theory.
WARNING: The course syllabus provides a general plan for the course; deviations may become necessary. ------------------------------------------ Last modified: September 20, 2023. |