Title: Partial chaos in dynamical systems: geometric origins

There are many important dynamical systems that are known to be chaotic. However, "chaos" is not a mathematical term. Instead, there are several related mathematical concepts that demonstrate chaos to some extent, such as
ergodicity, mixing, positive entropy, K property, Bernoulli property, Central limit theorem, etc. A system is partially chaotic if it has some of the properties from this list but not all. Partial chaos is much less understood than chaos. In this talk, I will present some new examples of partially chaotic systems. One example will be discussed in detail: a system based on the horocyle flow on a compact hyperbolic manifold, which has zero entropy but still satisfies the central limit theorem with the unusual scaling T/(log T)^{1/4}. This is a joint work with D. Dolgopyat, D. Dong and A. Kanigowski.