Report 39/2005: Analysis and Geometric Singularities (August 21st -- August 27th, 2005) (Q870681)

Summary: This workshop focused on several of the main areas of current research concerning analysis on singular and noncompact spaces. Topics included harmonic analysis and Hodge theory on, and the theory of compactifications of, locally symmetric spaces, new topological techniques in index theory, nonlinear elliptic problems related to metrics with special geometry, and various more traditional problems in spectral geometry concerning estimation of eigenvalues and the spectral function. Contributions: Bernd Ammann (joint with Emmanuel Humbert), The first Dirac eigenvalue in a conformal class (p. 2191); Ulrich Bunke, Aspects of equivariant twisted K-theory of Lie groups (p. 2194); Gilles Carron, \(L^2\) cohomology of QALE spaces(p. 2195); C. Robin Graham, Dirichlet-to-Neumann map for Poincaré-Einstein metrics (p. 2200); Daniel Grieser, Cheeger's inequality revisited (p. 2203); Eugénie Hunsicker, Interpolating L2 Hodge and Signature Theorems (p. 2205); Lizhen Ji, Compactifications of symmetric and locally symmetric spaces (p. 2208); Sergiu Moroianu (joint with Sylvain Golénia), On the essential spectrum of magnetic Schrödinger operators (p.2215); Werner Müller, Spectral theory on locally symmetric spaces (p. 2216); Frank Pacard (joint with C. Arezzo), Blowing up Kähler manifolds of constant scalar curvature (p. 2220); Iosif Polterovich (joint with Dmitry Jakobson), The spectral function and the remainder in local Weyl's law: View from below (p. 2224); Thomas Schick (joint with Bernhard Hanke, Paolo Piazza), Index theory, \(C^*\)-algebras and applications; a survey (p. 2225); Leslie Saper, \(L^2\)-harmonic forms on locally symmetric spaces (p. 2229); Michael A. Singer, Extremal Kähler metrics (p. 2230); Nader Yeganefar, Quadratic curvature decay and asymptotic cones (p. 2234); Hartmut Weiß (joint with Joan Porti in part), Rigidity of cone-3-manifolds (p. 2235)..