Some notes I wrote as a student in ancient times

• Formalism of mixed Hodge modules
• Equivariant perverse sheaves
• Springer's homotopy argument
• The degenerate affine braid group and generalized Schur-Weyl duality
• Generation and equivalences in abelian and triangulated categories (Warning: there are several typos in the proof of Lemma 0.11)
• The Octahedron axiom
• Derived categories cheatsheet
• Triangulated functor categories
• Bijective antipodes in Hopf algebras
• The determinant
• Category O; Some notes from a talk on the same
• Principal block of sl_2
• Trace in categories
• Adjoint functors
• Limits and adjoints
• Grothendieck group of the derived category
• Monoidal categories
• Jordan decomposition and Cartan's criterion
• 2x2 upper triangular matrices
• The Grothendieck group
• Weak sl_2 categorifications
• PBW theorem
• Dixmier's version of Schur's lemma
• Categories and functors
• Tensor products
• Quadratic reciprocity
• Real polynomials on the circle
• Minkowski's geometry of numbers; Slides for a talk
• Orbit-stabilizer theorem
• Completing the square
• Solving the cubic
• Graph homology
• Cohomology long exact sequence
• Nakayama's lemma
• Localization
• Cesaro summability of Fourier series

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Last updated: 15 April, 2008