Mathematical Physics

• Symmetries and conservations laws as basic tools in the investigation of physical systems: generalized symmetries on curved spaces, symmetry analysis of physical processes in external fields, general formalisms for the description of dynamics, singularities in general relativity and cosmological models

• Superstring theory (topological field theory, string field theory, dualities and conformal field theories, advanced mathematical methods in renormalization theory, extensions of combinatorial matrix models to the tridimensional case, singular space-times and black holes);

• Geometric methods in quantum physics, quantum optics, study of symmetries using theory of representations, geometry of coherent states, representations of Jacobi-type groups with applications to quantum squeezed states;

• Nonlinear integrable dynamical systems - discrete and supersymmetric integrability, cellular automata, resolutions of singularities and algebraic entropy using techniques from the algebraic geometry of rational elliptic surfaces, integrable soliton-hierarchies described by infinite-dimensional Lie algebras and super-algebras, integrability and super-integrability of geodesic equations on curved spaces with various geometries;

• Nonlinear dynamics of conservative and dissipative systems, localized structures in optics, fluids, plasma and interface plasma-short pulse lasers (study of soliton dynamics, pattern formations, stability, self-focusing, and weak (integrable) turbulence);