**Title:** Central Limit Theorem for equilibrium measures in dynamical systems

**Speaker: **Tianyu Wang – Ohio State University

**Abstract:** Central limit theorem of certain class of equilibrium measures is a heavily studied statistical property in smooth dynamics. In the first half of the talk, I will briefly introduce some common strategies to study CLT that are useful in many classic settings, e.g. Anosov flows, expanding maps on the unit circle, (countable) Markov shift, etc. In the second half, I will show how specification can be applied to derive an asymptotic version of CLT for the equilibrium measures in the case of geodesic flow on non-positively curved rank-one manifold. This method is first introduced by Denker, Senti, Zhang and the result is based on a recent joint work with Dan Thompson.