Slawomir Klimek Ph.D.

Associate Professor, Mathematical Sciences

Education

1988, Ph.D. at Warsaw University, Advisor: Dr. Kazimierz Napiorkowski, Thesis Title: A construction of two dimensional QCD

1983, M.Sc. at Warsaw University, Advisor: Dr. Witold Kondracki, Thesis Title: On theta-theories and multivalued wave functions

Prof. Klimek is trained as a mathematical physicist, and his research interests are rooted in problems from that area. His recent work developed a notion of noncommutative harmonic analysis which is likely to have many interesting applications. He has also done substantial work on index theory and dynamics in the context of noncommutative geometry and has recently become interested in the applications of these areas to number theory. He is unique in this area in that he is really trained as a physicist, but has a mathematician's taste in problems and methods.

Current Research

Prof. Klimek research focuses on the noncommutative geometry and its relation to modern theoretical physics. In collaboration with A. Lesniewski, David Borthwick, and Maurizio Rinaldi (Harvard University), he constructed several classes of fundamental examples including quantum Riemann surfaces, Cartan domains, and Dirac operators. He has also obtained a number of results in abstract cyclic cohomology theory in noncommutative spaces.

During recent years, Klimek has been publishing papers on mathematical aspects of quantum field theories, supersymmetry, mathematical quantization, quantum chaos, cyclic theory, eta invariants, infinite dimensional group actions Lie theory, and theory of operators on Banach and Hilbert spaces. He is currently working on concrete projects in quantum chaos, infinite dimensional geometry, and (almost periodic) field theory. Klimek is also actively pursuing the possibilities of applying noncommutative methods in number theory.

Select Publications

D-bar operators on quantum domains, with M. MacBride, arXiv:1001.2216 (2009) Math. Phys. Anal. Geom. 13, 357 – 390 (2010)

A note on Dirac operators on the quantum punctured disk, with M. MacBride, arXiv:1003.5618 (2010) SIGMA 6, 056 - 68 (2010)

Classical limit of the d-bar operators on quantum domains, with M. MacBride, arXiv:1101.2645 (2011) J. Math. Phys. 52, 093501 (2011)

Global boundary conditions for the Dirac operator on the solid torus, with M. MacBride, arXiv:1103.4569 (2011) , J. Math. Phys. 52, 063518 (2011)