### The Halász-Székely Barycenter

Ergodic Theory and Dynamical Systems Seminar

18th March 2021, 2:00 pm – 3:00 pm

Online, via Zoom

In this talk we will introduce a notion of barycenter of a probability measure related to the symmetric mean of a collection of nonnegative real numbers. Our definition is inspired by the 1976 work of Halász and Székely. We will describe some of the properties of this barycenter and go on to establish an ergodic theorem that relates the symmetric mean of a sequence of dynamical observations with the barycenter of an ergodic measure. This is joint work with Jairo Bochi and Mario Ponce.

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