MATH6209 - Special Topics in Mathematics: Dirac operators and Atiyah-Singer index theorem

Format:  10 two hour lectures and presentations. I will give six lectures covering Clifford algebras, spin groups and spinor representations, spin manifolds and Dirac operators, and the heat kernel proof of the Atiyah-Singer index theorem;  in between, participants will give presentations on the following topics

  •        Vector bundles, connections and curvatures;
  •        Fundamental theorem of Riemannian geometry: the existence of the Levi-Civita connections
  •        Example: Dirac operators on symmetric spaces
  •        Heat kernel on Rn

Time:  Friday 10-12 for ten weeks

Prerequisites:  linear algebra, multivariable calculus and some familiarity with the notion of smooth manifolds (a review of the latter subject can be done if demanded)

Lecturer: Bryan Wang


Updated:  22 February 2018/Responsible Officer:  Director/Page Contact:  School Manager