Title: Dynamical cohomology and Benford's first-digit law for the partial quotients of continued fractions.
Abstract: In a new preprint with Xuan Zhang, we give a proof of Benford's law for the partial quotients $q_n$ of the continued fraction expansion of a.e. real number $x\in (0,1)$. In this talk, I will first review the meaning of cohomology in ergodic theory, specifically for circle-valued skew product transformations, building on the work of Furstenberg. This leads to a characterization of those stationary processes for which the partial sums are uniformly distributed mod 1(if and only if a coboundary condition is satisfied). In the paper, we examine this condition for certain Gibbs-Markov maps and show that $\log q_n$ can be well enough approximated by such processes to yield Benford's law for $q_n$ itself.
