Calendar

Past topics

Ludicrous speed through scheme basics

Nov 23: Sheaves
Nov 30: Schemes
Dec 2: Projective spaces

Generation and representability

Nov 4: Serre functors
Nov 9: Brown representability
Nov 11: Strong generation and ghosts
Nov 16: Strong generation and saturation
Nov 18: Examples of strong generation

Semi-orthogonal decompositions

Oct 26: SODs and upper triangular algebras
Oct 28: Properties of SODs
Nov 2: Mutations and braid group actions

Derived Morita equivalences, dg-algebras, and integral transforms

Oct 12: Derived categories of dg-modules
Oct 14: Derived Morita equivalences and integral transforms
Oct 19: More on kernels, homological smoothness and properness
Oct 21: A look ahead to geometry

Compactly generated triangulated categories

Oct 5: Compact generators and resolutions

The derived category and derived functors

Sept 16: Triangulated categories
Sept 21: K-projectives and K-injectives
Sept 23: Derived categories
Sept 28: Derived functors
Sept 30: Derived tensor and Hom

Abelian categories and chain complexes

Sept 7: Abelian categories and (half) exact functors
Sept 9: Exactness for $\text{Hom}$ and $\otimes$: projectives, injectives, and flat modules
Sept 14: Homotopy category of chain complexes

Categories

Aug 24: Definitions of categories and examples
Aug 26: Functors, natural transformations, and equivalences
Aug 31: Adjunctions
Sept 2: Representable functors and Yoneda