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Contact information: Address: Vladimir V. Kisil   School of Mathematics   University of Leeds   Leeds LS2 9JT   UK phone: +44 113 343 5173 fax: +44 113 343 5090 Email: kisilv@maths.leeds.ac.uk Homepage: http://www.maths.leeds.ac.uk/~kisilv/

I am a Reader of Applied Analysis at Department of Pure Mathematics, University of Leeds.

My both MSc and PhD degrees in Mathematics were obtained from Institute of Mathematics, Economics, and Mechanics of Odessa National University named after I.I.Mechnikov—1908 Nobel Laureate in Medicine.

Current information:

• I wrote the book Geometry of Möbius Transformations. Here is an easy reading introduction. The book is supported by DVD, you can play with conic sections interactively.

  The wider context for the book is explained in the paper Erlangen Program at Large: an Overview.

• Is it true that Classical/Quantum=Commutative/Noncommutative?
• Localization technique introduced by I. B. Simonenko is connected with operator covariant transform produced by nilpotent Lie groups.
• New paper Computation and Dynamics: Classical and Quantum represents classical and quantum computations as Hamiltonian dynamics.

My research interests are (see also Information for Prospective Postgraduate Students):

• Operator and C*-algebras with symmetries, particularly algebra of convolutions and pseudodifferential 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 and Clifford analysis;
• Applications of coherent states, wavelet transform and group representations in quantum mechanics, combinatorics, etc.

Current and Past Research Students:

• Souad Abumaryam works on computational methods in harmonic analysis.
• Amer Albargi works on operators and wavelets.
• Abdelhamid El Mabrok works on Toeplitz operators and the affine group.
• Mohamed Bugatma worked on induced representations.
• Daniel Seidel worked on symbolic computations with GiNaC.
• Debapriya Biswas, thesis Geometry of elliptic, parabolic and hyperbolic homogeneous spaces using Clifford algebras and group representations (2006).
• Abd-Razak Ahmad (finished 2004).
• Alastair Brodlie, thesis Relationships Between Quantum and Classical Mechanics using the Representation Theory of the Heisenberg Group (2004).

Online materials of mathematical courses:

“Any teacher in the modern world who allows himself to be inspired by the ideals of his predecessors is likely to be made sharply aware that it is not his function to teach what he thinks, but to instill such beliefs and prejudices as are thought useful by his employers.”
  Bertrand Russell, The Functions of a Teacher.

You could also read:

• Information for Prospective Postgraduate Students.
• Complete List of Publications with hyperlinks to papers and reviews, also available in PDF, PostScript, and DVI formats.
• Curriculum Vita, also available in PDF, PostScript, and DVI formats.
• Some related links—a recommended way to leave my page.

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