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UID:20251220T153456EST-9295PnIMVS@132.216.98.100
DTSTAMP:20251220T203456Z
DESCRIPTION: \n\nTitle: An ergodic advertisement for descriptive graph comb
 inatorics\n\nAbstract\n\nDating back to Birkhoff\, pointwise ergodic theor
 ems for probability measure preserving (pmp) actions of countable groups a
 re bridges between the global condition of ergodicity (measure-transitivit
 y) and the local combinatorics of the actions. Each such action induces a 
 Borel equivalence relation with countable classes and the study of these e
 quivalence relations is a flourishing subject in modern descriptive set th
 eory. Such an equivalence relation can also be viewed as the connectedness
  relation of a locally countable Borel graph. These strong connections bet
 ween equivalence relations\, group actions\, and graphs create an extremel
 y fruitful interplay between descriptive set theory\, ergodic theory\, mea
 sured group theory\, probability theory\, and descriptive graph combinator
 ics. I will discuss how descriptive set theoretic thinking combined with c
 ombinatorial and measure theoretic arguments yields a pointwise ergodic th
 eorem for quasi-pmp locally countable graphs. This theorem is a vastly gen
 eral random version of pointwise ergodic theorems for group actions and is
  provably the best possible pointwise ergodic result for some of these act
 ions.\n\n \n\n \n
DTSTART:20181213T210000Z
DTEND:20181213T220000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Anush Tserunyan - Urbana-Champaign
URL:/mathstat/channels/event/anush-tserunyan-urbana-ch
 ampaign-292391
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