R440, Astronomy-Mathematics Building, NTU
Organizer(s):
Jiun-Cheng Chen (National Tsing Hua University)
Jungkai Chen (National Taiwan University)
Wu-yen Chuang (National Taiwan University)
Shin-Yao Jow (National Tsing Hua University)
Ching-Jui Lai (National Cheng Kung University)
Course Description:
Phase 1: Introductory to Abstract Algebra Constructions
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Homological Algebra: Ring and module, exact sequences, Hom and tensor, injective/projective/flat, free resolution, derived functors (Ext and Tor).
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Commutative Algebra: Local rings, Spec,
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Category Theory: Abelian Category, Localization construction, Triangulated Category
Phase 2: Introductory to Algebraic Geometry
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Algebraic Geometry: Varieties, Scheme, Sheaves, and cohomology theory
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Cohomology and base change theorem
Phase 3: Introductory to Derived Category
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Category of sheaves
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Derived Category in Algebraic Geometry
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Semi-orthogonal decomposition
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Fourier-Mukai transforms
Phase 4: Advanced Topics
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Fourier-Mukai transforms on Abelian varieties
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Derived Category of Toric Varieties
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Bridgeland stability conditions
Contact:
murphyyu@ncts.ntu.edu.tw
