The spectral localizer of an index pairing (Guest seminar - joint with the Oberseminar Global Analysis and Operator Algebras of the MI Bonn)

Guest seminar (joint with the Oberseminar Global Analysis and Operator Algebras of
the MI Bonn)

Abstract: Index pairings are integer-valued homotopy invariants combining a Fredholm module
with a K-theory class specified by a projection or a unitary. Numerous classical examples
are known from differential and non-commutative geometry and physics. In this talk we
discuss the spectral localizer, a finite dimensional matrix whose signature computes the
index pairing explicitly. This makes the invariant numerically accessible.