# Slawomir Klimek

Associate Professor, Department of Mathematical SciencesProf. Klimek is trained as a mathematical physicist, and his research interests are rooted in problems from that area. His recent work pursues parallels between theory of Riemann surfaces and the theory of number fields in the context of noncommutative geometry. He has also done substantial work on index theory and infinite dimensional geometry and analysis.

## 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

## Research

Prof. Klimek research focuses on the noncommutative geometry and its relation to modern theoretical physics and number theory. He constructed several classes of fundamental examples including quantum Riemann surfaces, Cartan domains, and noncommutative analogs of Dirac operators. He has also obtained a number of results in diverse area of modern analysis. 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 and Lie theory, and theory of operators on Banach and Hilbert spaces. He is currently working on construction of spectral triples for quantum surfaces and also for p-adic number theoretic systems.

## Publications & Professional Activities

- S. Klimek, M. McBride, A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere, arXiv:1309.7096 (2013), SIGMA 10, 036 (2014)
- S. Klimek, M. McBride, S. Rathnayake, A p-adic spectral triple, arXiv:1403.7263 (2014), J. Math. Phys. 55, 113502 (2014)
- S. Klimek, M. McBride, S. Rathnayake, K. Sakai, Quantum pair of pants, arXiv:1410.0733 (2014), SIGMA 11, 012 (2015)
- S. Klimek, S. Rathnayake, K. Sakai, A note on the spectral properties of the p-adic tree, arXiv:1503.03053 (2015), J. Math. Phys. 57, 023512 (2016)