• I gave a presentation at Boston College's Undergraduate Math Colloquium on Knots and Curve Singularities: [Slides], [Website]
• Notes from a class in Fall 2026 on intersection homology, perverse sheaves, and the decomposition theorem:
  • 1. Mortivation: Polytopes and intersection homology
  • 2. Topology of Whitney stratifications
  • 3. Intersection homology: Definitions and first examples
  • 4. Normalizations
  • 5. Intersection homology of cones, Mayer-Vietoris, Borel-Moore homology
  • 6. Poincare duality and the middle perversity
  • 7. Local systems and constructibility
  • 8. Derived categories and derived functors
  • 9. Six functor formalism and Verdier duality
  • 10. The intersection coholomology complex: Definition via cycles, Deligne's construction, and duality
  • 11. Intrinsic axioms for intersection cohomology and independence of stratification
  • 12. t-structures and perverse sheaves
  • 13. Intersection cohomology on curves and other computations
  • 14. Intermediate extensions and simple perverse sheaves
  • 15. Splitting principle and Artin's vanishing theorems for perverse sheaves