Selected Aspects of the Mathematical Work of Krzysztof P. Wojciechowski

Abstract

I review the milestones of the mathematical work of Krzysztof P. Wojciechowski. This will at the same time be a tour of Analysis and Geometry of Boundary Value Problems. Starting in the 80s I will discuss the spectral flow and the general linear conjugation problem, the Calderon projector and the topology of space of elliptic boundary problems. The theme of the 90s is the eta invariant. The paper with Douglas was fundamental for establishing spectral invariants for manifolds with boundary and for the investigation of the behavior of spectral invariants under analytic surgery. This was so influential that many different proofs of the gluing formula for the eta-invariant were published. Finally turning to the new millennium we will look at the zeta--determinant. Compared to eta this is a much more rigid spectral invariant which is technically challenging. This paper was presented at the workshop "Krzysztof Wojciechowski - 50 Years" held in May 2005 near Roskilde/Denmark.