On a noncommutative Tannaka-Krein duality principle

Abstract: The Tannaka-Krein duality theorem states that any compact group can be recover from its category of finite-dimensional representations. The importance of this theorem is related to some questions in abstract harmonic analysis, operator algebras and mathematical physics. Moreover, nowdays this theorem has also gained importance because it is the key idea of the Tannakien formalism in modern algebraic geometry. In this talk, I will survey the (commutative) Tannaka-Krein duality principle and then, in a second time, I will present the ideas and some results in the noncommutative case.