Homogeneous Flows, Moduli Spaces and Arithmetic

abstract: In this talk, I will develop a systematic theory of pseudo--measures on $P1(R)$ which extends the well--known formalism of modular symbols for $SL(2)$ and its more recent iterated version. It can be considered as an $\infty$-adic analog of Mazur's p-adic measures, and it comes together with a Mellin-Levy transform, similar to the p-adic Mellin-Mazur transform. The talk is based on a recent paper written jointly with Matilde Marcolli.