Let M1 and M2 be two Riemannian manifolds each of which have the boundary N. Consider the Laplacian on M1 and M2 augmented with Dirichlet boundary conditions on N. A natural question to ask is if there is any relation between spectral properties of the Laplacian on M1, M2, and the Laplacian on the manifold M (without boundary) obtained gluing together M1 and M2, namely M = M1 ∪N M2. Using spectral zeta functions, a partial answer is given by the Burghelea-Friedlander- Kappeler-gluing formula for zeta-determinants. This formula contains an (in general) unknown polynomial which is completely determined by some data on a collar neighborhood of the hypersurface N. I will use conformal transformations to understand the geometric content of this polynomial. The understanding obtained will pave the way for a fairly straightforward computation of the polynomial (at least for low dimensions of M). Furthermore it leads to a partial understanding of the heat invariant for the Dirichlet-to-Neumann map, that is for the Steklov problem. Speaker(s): Klaus Kristen (Mathematical Reviews AMS and Baylor University)