Algebraic structures in quantum field theories

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The central topic of my research interests revolves about the symmetries of Nature and the relations between these symmetries. More specifically, I study kinematical algebras such as Poincaré algebra (which underlies all relativistic theories), Galilei algebra (fundamental in Newtonian physics), de Sitter (with relativistic curved space-time), Newton-Hooke (non-relativistic curved space-time), etc. The mathematical procedures which connect these symmetries are called "contractions" and "deformations" of Lie algebras. In principle, they allow one to deduce further knowledge about some symmetries from the associated symmetries. I will apply these techniques to other types of symmetries such as the infinite-dimensional Lie algebras which occur in conformal field theories such as string theory or the critical phenomena of statistical physics.