Analysis on singular and non-compact spaces: a C*-algebra approach – SINGSTAR

Many problems in Mathematical Physics, Number Theory, Geometry, Partial Differential Equations and other areas of science lead to advanced questions in Functional Analysis. An example of such a question is to understand analysis on non-compact and singular spaces. Classical analysis on euclidean spaces or bounded domains can be modeled by either commutative $C^*$-algebras or by the algebra of compact operators, and both of these are examples of operator algebras that correspond to groupoids. We plan to use larger classes of groupoids to model many of the singular spaces that arise in applications. In addition to groupoids, we shall also consider other tools of noncommutative geometry, such as $C^*$-algebras, $K$-theory, and cyclic homology. Natural questions to study are those related to the index and the eta-invariants of the corresponding elliptic operators, the Hadamard
well-posedness of the resulting equations, and applications of such operators.