Dear all, This week, Friday July 3, Davide Ravotti (Monash University) will give a talk at 4pm (Sydney time) via Zoom. Zoom link: https://uni-sydney.zoom.us/j/91246625911 Meeting ID: 912 4662 5911 Title: Quantitative global-local mixing for accessible skew products Abstract: Skew products, or group extensions, over hyperbolic diffeomorphisms are important examples of partially hyperbolic systems. Dolgopyat showed that generic compact extensions of topologically mixing Axiom A diffeomorphisms are rapidly mixing, namely the decay of correlations of smooth observables is faster than any given polynomial. In this talk, we will consider the case of $\mathbb{R}$-extensions. We will focus on global-local mixing, one of the possible notions of mixing for infinite measure preserving systems. We will present a quantitative mixing result for skew products which satisfy an accessibility condition; in particular, we will relate the rate of decay of correlations to the ’’low frequency behaviour’’ of the spectral measure associated to our global observables. This is a joint work with Paolo Giulietti and Andy Hammerlindl. Past talks can be found on the YouTube channel: https://www.youtube.com/channel/UCZqgDJ21wbdzMbeIdealpUg/ I hope to see you all online. Lachlan