Foundations of quantum mechanics;
Integrable and superintegrable models;
Symmetries of nonlinear differential equations;
Infinite-dimensional symmetries ;
Duality in quantum field theory and quantum mechanics;
Superstrings, cosmology, quantum gravity and topological defects;
Group theory in modern geometry, noncommutative geometry;
Loop algebras and W-algebras;
Lie groups, representation theory and special functions;
Quantum optics and quantum information;
Symmetry aspect of classical and quantum chaos;
Symmetries in particle, nuclear, atomic and molecular physics;
Symmetries in condensed matter physics and statistical physics.
Modern application of group theory in biology.
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