Dr Vladimir V. Kisil
Mathematics is a unified subjects and the concept of symmetry links together various areas. Applications in physics and other sciences provide a rich source of intriguing questions and inspiring hints for their solutions.
Applications of symmetries and group representations in geometry, complex analysis, operator theory, functional calculus and spectra. In particular:
- C*-algebras with symmetries, particularly algebra of convolutions and pseudo-differential operators on Lie groups and homogeneous spaces;
- Functional calculus of operators and associated notions of (joint) spectrum of operators;
- Hilbert spaces of analytic functions with reproducing kernels arising from group representations in complex, hypercomplex and Clifford analysis;
- Applications of coherent states, wavelet transform and group representations in quantum mechanics, foundations of quantum mechanics;
- Non-commutative geometry of homogeneous space based on the Erlangen programme;
- Cancellative semigroups and umbral-type calculus in combinatorics, mathematical physics and analysis.
Research groups and institutes
- Pure Mathematics