**Week 1 (20 Jun-25 Jun):**general preview on HMS (Peize); symplectic geometry (Dekun); simplicial categories, basics in complex geometry (Jinghui).**Week 2 (27 Jun-1 Jul):**triangulated categories, derived categories, differential graded categories (Shuwei). \( A_\infty \)-algebras and \( A_\infty \)-categories (Peize).**Week 3 (4 Jul-8 Jul): Break! No meeting this week.****Week 4 (13 Jul-15 Jul):**Hodge theory on closed Riemannian and Kähler manifolds (Jinghui).**Week 5 (18 Jul-22 Jul):**Floer homology (Dekun).**Week 6 (25 Jul-29 Jul)**: moduli spaces, Floer homology (continued), operads (Dekun). derived categories, Kan extension, derived functors as Kan extensions, Ext and Tor (Peize).**Week 7 (1 Aug-5 Aug)**: review of scheme theory, (quasi-)coherent sheaves, smoothness, perfect complexes, Serre duality, Grothendieck-Verdier duality, Bondal-Orlov reconstruction theorem, Fano varieties, \( A_{\infty} \)-structure on \( \text{Coh}(X) \) (Peize). Algebraic operads (Shuwei).**Week 8 (8 Aug-12 Aug)**: Morse theory and the symplectic quotient (Dekun); algebraic operads (continued, Shuwei); Bondal-Orlov reconstruction from derived categories (Peize).**Week 9 (15 Aug-19 Aug)**: homotopical algebra, algebraic K-theory, intro to Dennis trace method (Jinghui). quiver and quiver representations (Shuwei).**Week 10 (22 Aug-26 Aug)**: Derived categories, Beilinson resolutions, Baer-Bondal, quiver representations (Peize). Intro to homotopy type theory (Jinghui). Brief computation recipes to HMS for 3-torus (Dekun).**Seminar paused due to personal reasons.**

**Week 1 (20 Jun-25 Jun):**

- [
**Bocklandt**] A Gentle Introduction to Homological Mirror Symmetry . General Introduction to the Homological Mirror Symmetry Theory. - [
**Auroux**] A beginner's introduction to Fukaya categories . This is an introduction to the Fukaya Category. - [
**Joyce**] Riemannian holonomy groups and calibrated geometry . Chapter 9 of this book serves as an interesting motivation for our topic.

- Math 595: Homological Mirror Symmetry (Spring 2018). Taught by Prof. James Pascaleff, University of Illinois, Urbana-Champaign.
- Lectures on Homological Mirror Symmetry. Taught by Dr. Nick Sheridan at IAS.