Graduate Analysis Seminar:18.199 (Spring 2006)

Dirac Operators

• Organizational meeting -- my office (2-174) 4PM Feb 7, 2006.
• 9 February, 2006: I will give an overview of Dirac operators
• 14 February, 2006: No meeting.
• 16 February, 2006:
  • Ricardo Andrade:- Clifford algebras
  • Yakov Shapiro:- Clifford modules
• 21 February, 2006: No meeting, an MIT Monday.
• 23 February, 2006:
  • William Lopes:- Examples, signature, $\dbar+\dbar^*,$ Gauss-Bonnet
  • Zuoqin Wang:- Lichnerowicz formula.
  • (maybe) Yakov Shapiro:- $\bbZ_2$ grading.
• 28 February, 2006:
  • Ricardo Andrade:- Periodicity
  • Fangyun Yang:- Elliptic regularity
  • Maksim Lipyanskiy:- Spin representation
• 2 March, 2006:
  • Maksim Lipyanskiy:- Spin and Spin-C structures
  • Yakov Shapiro:- grading
  • William Lopes:- Complex case.
  • Me:- Azumaya bundles.
• 7 March, 2006
  • Ricardo Andrade:- Unique continuation.
  • Zuoqin Wang:- Heat kernel (in part)
• 14 March, 2006
  • William Lopes:- Linearization of loops.
  • Yakov Shapiro:- Chern classes.
• 16 March, 2006
  • Yakov Shapiro:- Chern classes.
  • Maksim Lipyanskiy:- Impromtu discussion of McKean-Singer
  • William Lopes:- Linearization of loops.
• 20 March, 2006
  • Ricardo Andrade:- Mehler's formula
  • Fangyun Yang:- Eta invariant
• 23 March, 2006
  • Ricardo Andrade:- Local index theorem
• 4 April, 2006
  • Fangyun Yang:- Eta invariant, cont.
• 6 April, 2006
  • Maksim Lipyanskiy:- Index theorem via principal bundle.
  • Zuoqin Wang:- Zeta function
• 11 April, 2006
  • Yakov Shapiro:- Determinant bundle
  • Zuoqin Wang:- Zeta function, conclusion
• 13 April, 2006
• 20 April, 2006
  • Ricardo Andrade:- index theorem of Atiyah, Patodi and Singer
• 27 April, 2006
  • Zuoqin Wang:- Analytic torsion (cont)
  • Fangyun Yang:- Families index theorem (cont)
• 2 May, 2006
  • Yakov Shaprio:- Curvature of the determinant bundle
  • Jonathan Campbell:- Suspension and η
• 4 May, 2006
  • Me:- Topological formulation of the Atiyah-Patodi Singer index theorem.
• 9 May, 2006
  • Maksim Lipyanskiy:- Bott periodicity and the index
• 11 May, 2006
  • Zuoqin Wang:- Cheeger-Mueller theorem.
• 16 May, 2006 -- no meeting.
• 18 May, 2006 -- Ended with a whimper, since no one was prepared to speak!
  • Ricardo Andrade:- Dirac on loop spaces
  • Fangyun Yang:- Adiabatic limit of eta
  • Maksim Lipyanskiy:- G-equivarant index