Seminar at SMU Delhi

Let $\gamma$ be a ( possibly non abelian ) countable discrete group. Motivated by the construction of the Dirac operator, Connes attaches a spectral data to the group $\gamma$, which comes from some length function. It is a striking fact that this spectral data remembers some properties (like growth ) of the group. The spectral data gives rise to analogues of metric spaces for the noncommutative space given by the group ring of $\gamma$.