Potential talk topics

  • Principal bundles and classifying spaces
  • Spin, spin^c, Clifford multiplication
  • Spinor bundles and Dirac operators
  • Fredholm operators and the Atiyah-Singer Index Theorem
  • SW equations, monopole map and Coulomb gauge slice
  • Equivariant Seiberg-Witten Floer theory
  • Vector fields on manifolds and index
  • Morse theory and the Cohen-Jones-Segal construction
  • Conley Index Theory
  • Equivariant cohomology
  • Stable homotopy theory 1 - basic
  • Stable homotopy theory 2 - invariants and Spanier-Whitehead duality
  • The Seiberg-Witten Floer stable homotopy type
  • The triangulation conjecture 1 - manifold structures, Kirby-Siebenmann and Rochlin invariants
  • The triangulation conjecture 2 - history of the triangulation problem and the Hauptvermutung
  • The triangulation conjecture 3 - solution by Casson and Manolescu