Room 440, AstronomyMathematics Building, NTU
(台灣大學天文數學館 440室)
Taiwan Math School: Derived and Homological Algebraic Geometry
Jungkai Chen (National Taiwan University &
NCTS)
Course Description:
Phase 1: Introductory to Abstract Algebra Constructions

Homological Algebra: Ring and module, exact sequences, Hom and tensor, injective/projective/flat, free resolution, derived functors (Ext and Tor).

Commutative Algebra: Local rings, Spec,

Category Theory: Abelian Category, Localization construction, Triangulated Category
Phase 2: Introductory to Algebraic Geometry

Algebraic Geometry: Varieties, Scheme, Sheaves, and cohomology theory

Cohomology and base change theorem
Phase 3: Introductory to Derived Category

Category of sheaves

Derived Category in Algebraic Geometry

Semiorthogonal decomposition

FourierMukai transforms
Phase 4: Advanced Topics

FourierMukai transforms on Abelian varieties

Derived Category of Toric Varieties

Bridgeland stability conditions
Time: From 10/27 to 12/15(Every Friday) 10:0012:00