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Logic Seminar

Wednesday, November 4, 2020
12:00pm to 1:00pm
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A backward ergodic theorem and its forward implications
Anush Tserunyan, The Department of Mathematics and Statistics, McGill University,

In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation TT, one takes averages of a given integrable function over the intervals {x,T(x),T2(x),…,Tn(x)}{x,T(x),T2(x),…,Tn(x)} in front of the point xx. We prove a "backward" ergodic theorem for a countable-to-one pmp TT, where the averages are taken over subtrees of the graph of TT that are rooted at xx and lie behind xx (in the direction of T−1T−1). Surprisingly, this theorem yields forward ergodic theorems for countable groups, in particular, for pmp actions of finitely generated groups, where the averages are taken along set-theoretic (but backward) trees on the generating set. This strengthens Bufetov's theorem from 2000, which was the leading result in this vein. This is joint work with Jenna Zomback.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit https://caltech.zoom.us/j/82512909111?pwd=aUJpWkF1WThBNFQ0TjFRR3pOd2svUT09.