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Accueil > Research teams > Algèbre, topologie, groupes quantiques, représentations > Topics of interests

Topics of interests    fr

The topics of interests to the members of the "Algèbre, topologie, groupes quantiques, représentations" team are of two kinds: some lie at the interface between algebra and another subject, while others are purely algebraic.

Thus several of us are interested in algebraic topology (stable homotopy, group cohomology), or low-dimensional topology (knot theory and also quantum topology).

Work in this area stimulates the development of algebraic tools, such as operads, Hopf algebras, or quantization, which are all subjects of study in their own right within our group.

Research has started recently on the topic of cluster algebras. Connections with theoretical physics and quantum groups are also envisaged.

Other members of our team study questions in harmonic analysis (representations of semi-simple groups, zeta functions, pre-homogeneous spaces). Again algebraic techniques are used and expanded, such as Lie and Kac-Moody algebra theory, or Howe duality.