Salinas will continue his research on Toeplitz C*-algebras over domains with non-abelian symmetries, spectral and C*- algebraic properties of Toeplitz operators on pseudoconvex domains, and weighted Wiener-Hopf operators on convex cones. Upmeier will continue his study of quantization theories in several complex variables with the main focus on new geometric situations. He will also study new types of special functions arising in quantization theory, and deepen the connections with microlocal analysis. Operator theory is that part of mathematics that studies the infinite dimensional generalizations of matrices. In particular, when restricted to finite dimensional subspaces, an operator has the usual linear properties, and thus can be represented by a matrix. The central problem in operator theory is to classify operators satisfying additional conditions given in terms of associated operators (e.g. the adjoint) or in terms of the underlying space. Operator theory underlies much of mathematics, and many of the applications of mathematics to other sciences.
