241C: Introduction to Dirac Operator and Atiyah-Singer Index
Theorem
MWF 11-11:50 in SH 4607; prerequisite: 240A or consent of instructor
Office Hours: MWF 1-2pm or by appointment
The Atiyah-Singer index theorem is truely one of the great
landmarks of twentieth century mathmatics, a "grand unification" of the
classical Gauss-Bonnet-Chern formula, the Riemann-Roch formula and Hirzebruch's
signature formula, with broad applications in differential geometry, topology,
algebraic geometry, representation theory, number theory, and physics.
The Dirac operator is crucial in both the discovery and the proof of the
Atiyah-Singer index theorem. Moreover, the Dirac operator has become a
prominent player in both mathematics and physics. This course is
an introduction to Dirac operator, spin geometry and
Atiyah-Singer index theorems.