A Fixed-point Formula for Non-elliptic Dirac OperatorsOberseminar Global Analysis and Operator Algebras

by Ahmad Reza Haj Saeedi Sadegh (Dartmouth College)

Tuesday Jul 8, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Seminar room 1.008 (Mathezentrum)

We utilize the differential geometry of Lie algebroids to define not-necessarily elliptic Dirac operators. We will see that this construction is equivalent to a family of elliptic Dirac operators on source fibers of a Lie groupoid. Using trace pairing with K-theory we give a fixed-point formula for equivariant index of such Dirac operators. This result recovers Connes longitudinal index theorem for foliations, and we give a new example for manifold with normal crossing divisors.