Symmetries and geometry

We focus on the use of symmetries in the analytical and numerical solution of differential equations or in the construction of models in string theory. We also explore related areas of differential geometry and algebra, i.e. in particular the structure and applications of Lie groups and their algebras. We classify various special classes of Lie algebras, study them and use them in applications such as the construction of special functions or the study of models in string theory.

We look for groups of symmetries of interesting differential equations and use them in their solution. Conversely, we construct equations with selected symmetries and study their common properties. Using symmetries of simple Lie algebras, we investigate properties of symmetric functions of several variables and the corresponding orthogonal polynomials. We formulate their discrete Fourier analysis and test applications to digital data processing.

Staff