Klimek will continue his study of noncommutative geometry and the theory of infinite dimensional spaces. Of particular interest will be the construction of quantum Riemann surfaces and other noncommutative spaces, and application of the constructive field theory methods to analysis on infinite dimensional manifolds. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.
