Sylvie Paycha (Potsdam)

The Wodzicki residue; a useful analytic tool for geometric purposes

Abstract: The Wodzicki residue is a useful analytic tool to capture geometric information. Using the inverse Mellin transform, one can express the singular part as well as the constant term of the heat-kernel expansion on a closed manifold in terms of Wodzicki residues. This extends to two rather different geometric frameworks; the noncommutative torus on the one hand and Hilbert modules on the other. We revisit Atiyah's L^2-index theorem by means of the (extended) Wodzicki residue and inspired by Connes et al., define scalar curvature on the noncommutative two torus as an (extended) Wodzicki residue. Based on joint work with Sara Azzali, Cyril LÚvy and Carolina Neira-Jimenez.