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.

     ⋅  Date&Time: Every Friday 10:00 ~ 12:00, starting from 17 Oct

     ⋅  Place: Room 0.008, Endenicher Allee 60

     ⋅  Plan:

   I. Introduction and motivation

   II. Review of Morse theory and Lagrangian Floer theory

   III. A_infinity categories

   IV. Fukaya categories of symplectic manifolds and general statements of HMS

   V. HMS of graded surfaces, gentle algebras, and non-commutative curves

   VI. HMS of matrix factorizations and singularity categories

⋅  Main reference: [Bocklandt] A gentle introduction to homological mirror symmetry

⋅  Prerequisites:

  - basics in symplectic geometry (recommended)

       - basics in homological algebra (1-category theory + definition of derived categories)

  - basics in algebraic geometry (schemes, coherent sheaves)