Mathieu Helfter (Sorbonne University):

Title: "Scales: On the size of infinite dimensional spaces"

Abstract: Scales are finite bi-Lipschitz invariants that propose a generalization of a part of dimension theory, mostly for infinite dimensional spaces, possibly endowed with a measure. Scales exist of different kind: Hausdorff, packing, box, quantization, local, etc. and of different growths to describe spaces with various sizes. The comparisons between the different kind pf scales extend classical results of dimension theory  to any growth. We will use those new tools to describe the largeness of ergodic decompositions and functional spaces; or to study the behavior of the Wiener measure.