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
Current postgraduate research students
Postgraduate research opportunities
We welcome enquiries from motivated and qualified applicants from all around the world who are interested in PhD study. Our research opportunities allow you to search for projects and scholarships.
Projects currently available: