On extensions of Index=Spectral Flow beyond the Fredholm caseOberseminar Global Analysis and Operator Algebras

by Oliver Fürst (Mathematisches Institut)

Tuesday Oct 20, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

For a family $A(t)$, $t\in\mathbb{R}$, of self-adjoint operators
in Hilbert space $H$ we consider the perturbed differential operator
$D=\partial_{t}+A(t)$ acting in L^2(\mathbb{R},H)$. This so called
Robbin-Salamon type operator has been prominently studied in the context
of the Atiyah-Patodi-Singer index theorem and led to the invention of the
spectral flow of a Fredholm family of operators.
In this talk we will present a new result beyond the Fredholm case. We
will show that a wide range of useful examples for the family $A$ are now
amenable, among which are perturbed fractional Laplacians, certain
symmetric hyperbolic systems and conformal families of Dirac operators.

This is joint work with Jilly Kevo (IAM Bonn)