Lecture Series & Course
Lecture Series & Course
∎ Poisson Geometry and Integrable Systems, Universität Paderborn, 2023.12 ~ 2024.02 + 2024.07.
- I. Lagrangian mechanics (notes)
- II. Hamiltonian mechanics (notes)
- III. Integrability of rigid body problems (notes)
- IV. Integrability of high-dimensional rigid bodies (notes)
∎ Category of triples and mirror symmetry, Universität zu Köln, 2025.03 ~ 2025.04.
- I. Gentle algebras and hereditary envelopes (notes)
- II. Category of triples and matrix problems (notes)
- III. Representations of bunches of chains (notes)
- IV. Indecomposables in derived categories of gentle algebras (notes)
- V. Fukaya categories of surfaces (notes)
- VI. Homological mirror symmetry of gentle algebras and surfaces (notes)
∎ Fukaya categories and homological mirror symmetry, Universität Bonn, 2025.10 ~ 2026.02.
I. Introduction and motivation (notes)
II. Morse theory and Lagrangian Floer theory (notes)
III. A∞-categories (notes)
IV. Fukaya categories of symplectic manifolds (notes)
V. HMS of graded surfaces, gentle algebras, and nodal curves (notes)
⋅ Main references:
- [Auroux] A beginner's introduction to Fukaya categories
- [Bocklandt] A gentle introduction to homological mirror symmetry
- [Fukaya&Oh&Ohta&Ono] Lagrangian intersection Floer theory
- [Ganatra&Pardon&Shende] Covariantly functorial wrapped Floer theory on Liouville sectors
- [Keller] Introduction to A-infinity algebras and modules
- [Seidel] Fukaya categories and Picard-Lefschetz theory
⋅ Prerequisites:
- basics in symplectic geometry (recommended)
- basics in homological algebra (1-category theory + definition of derived categories)
- basics in algebraic geometry (schemes, coherent sheaves)
∎ Fukaya categories of surfaces and gentle algebras, Universität Paderborn, 2026.03.
- I. Introduction and motivation (notes)
- II. Fukaya categories of graded marked surfaces (notes)
- III. A∞-categories and derived categories (notes)
- IV. HMS of gentle algebras (notes)