Key results in physics and mathematics

1. New explicit relationship between analytical properties of meromorphic  functions on Riemann surfaces and differential-geometric characteristics of these surfaces >>

2. Prediction of phase transitions in systems of Charge Transfer Excitons (due to Prof. V.M. Agranovich) on organic interfaces >>

3. Quantum Gravity in non-homogeneous Bose condensates. Dualism of Macro and Micro >>

4. Exact Analytical solution of 1-dimensional XY model with arbitrary boundary conditions in final volume and at finite temperature. First explicitly solvable example of non-trivial quantum statistics in 1 dimension >>

5. Functional integral representation of classical mechanics: new correspondence between integrable classical systems in arbitrary dimensions and exactly solvable functional integrals >>

6. Analytical ground state of first experimental Bose-condensed atomic cloud >>

7. Constraint-free bosonization of spin systems in any dimension >>

8. Novel approach to modeling of dynamical systems of quasi-particles with slow creation/annihilation (retardation) by using q-deformed quantum statistics (quantum group particles or q-particles) >>

Other papers of KI treated particular aspects of high temperature superconductivity, condensed matter physics, quantum optics, mathematical physics, differential geometry are more specific in nature

Kirill Ilinski