Professor Alexandar Balinsky
Position:
WIMCS Research Chair in
Mathematical Physics
Email:
balinskyA@cardiff.ac.uk
Telephone:
+44(0)29 208 75528
Fax:
+44(0)29 208 74199
Extension:
75528
Location:
M/2.35
Analysis and Differential Equations
Balinsky A, Evans W D, Hundertmark D and Lewis R T, On Inequalities of Hardy-Sobolev Type, Banach J. Math. Anal. 2 (2008), no. 2, 94-106.
Balinsky A, Evans W D and Saito Y, Dirac–Sobolev inequalities and estimates for the zero modes of massless Dirac operators, J. Math. Phys. 49, (2008) (10 pages).
Balinsky A and Balinsky H, Affine invariant total variation models, In Proc. of The 10th IASTED International Conference on Computer Graphics and Imaging ,February 13 – 15, 2008 , Innsbruck, Austria.
Balinsky A and Ryan J, Some Sharp $L^{2}$ Inequalities for Dirac Type Operators, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), December 2007.
Balinsky A and Balinsky H, Affine Invariant Total Variation Models, Research Disclosure, 2007, N. 519, ISSN 0374-4353.
Balinsky A and Tyukov A,
On localization of pseudo-relativistic energy, Proc. Royal Society,
Mathematical, physical and engineering sciences, 2006, vol. 462,
no2067, pp. 897-912
Balinsky A and Tyukov A,
On Hardy type inequalities. Recent advances in differential equations and
mathematical physics, 69--77,
Contemp. Math., 412, Amer. Math. Soc., Providence, RI, 2006.
Balinsky A, Laptev A and Sobolev A V, Generalized Hardy
inequality for the magnetic Dirichlet forms, J. Statist. Phys. 116
(2004), no. 1-4, 507--521.
Balinsky A, Hardy type inequalities for Aharonov-Bohm magnetic
potentials with multiple singularities, Math. Res. Lett. 10 (2003),
1-8.
Balinsky A and Evans W D,
Zero modes of Pauli and Weyl-Dirac operators. Advances in differential
equations and mathematical physics (Birmingham, AL, 2002), 1--9, Contemp.
Math., 327, Amer. Math. Soc., Providence, RI,2003.
Balinsky A and Evans W D, On the zero modes of Weyl-Dirac
operators and their multiplicity, Bull. London Math. Soc. 34 (2002),
no. 2, 236--242.
Balinsky A and Evans W D, On the spectral properties of the Brown-Ravenhall operator, J. Comput. Appl. Math. 148 (2002), no. 1, 239—255.
MA0376 Mathematical Foundations of Internet Security
School IT Committee
WIMCS Research Chair in Mathematical Physics
Cardiff has one of the largest research groups in spectral theory of differential operators in the world. Our work on spectral theory informs and uses the results of vigorous activity in closely related areas such as function spaces, integral operators and geometry. Our overall strength across analysis creates a vibrant environment, attractive to visitors and to top-calibre new appointees alike, in which collaborative research, both inside and outside Cardiff, thrives. We work closely with the research groups at, among others, Birmingham (Alabama), Karlsruhe, Moscow State, Weizmann Institute, St. Petersburg, Bern, Santiago, Pisa, Montréal, McGill, Toulon and Marseilles.
We have been exceptionally active in organising workshops and conferences, to the benefit of the worldwide spectral theory community. Examples are:
a recent six-month programme on Analysis on Graphs at the Isaac Newton Institute;
EPSRC funded UK Spectral Theory Network, 2001-04;
triennial international Gregynog Workshops on Differential Equations since 1983, supported by EPSRC;
LMS supported workshop on “Analytical and numerical aspects of periodic PDE”, Cardiff, 2007;
three conferences in Cardiff in 2002 and 2004 in honour of MSP Eastham, WN Everitt and EB Davies.
The main directions of research in the Analysis and Differential Equations Group include:
Spectral theory of differential operators on domains, manifolds and graphs, including operators arising in mathematical physics and non-self-adjoint problems;
Universal and isoperimetric inequalities for eigenvalues;
Function spaces & integral operators,
Computational spectral theory
Inverse problems
Applications in mathematical bioinformatics; internet security and risk management; archaeology; image recognition; oceanology.
We work on a wide range of applications of differential equations and spectral theory, including problems arising in elasticity, hydrodynamics, electromagnetism, mathematical bioinformatics, internet security.