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SUMMARY:Sarah Peluse (Stanford University)
DTSTART:20260604T150000Z
DTEND:20260604T160000Z
DTSTAMP:20260604T173047Z
UID:NTWebSeminar/303
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTWebSeminar
 /303/">"The multilinear circle method" and pointwise ergodic theory</a>\nb
 y Sarah Peluse (Stanford University) as part of Number Theory Web Seminar\
 n\n\nAbstract\nIn 1975\, Szemer\\'edi proved that any subset of the natura
 l numbers with positive upper density must contain arbitrarily long finite
  arithmetic progressions. Szemer\\'edi's original argument was purely comb
 inatorial\, and then Furstenberg gave an alternative proof using ergodic t
 heory a couple of years later. Objects called "nonconventional ergodic ave
 rages" appeared for the first time in Furstenberg's proof\, and understand
 ing the limiting behavior of very general such averages became an importan
 t problem in ergodic theory. After breakthrough work of Bourgain in the la
 te 1980s and early 1990s\, no further progress had been made on proving po
 intwise almost everywhere convergence of these averages until recently. I 
 will report on this progress\, along with some of the key inputs from addi
 tive combinatorics\, focusing on very recent joint work of mine with Dariu
 sz Kosz\, Mariusz Mirek\, Renhui Wan\, and Jim Wright addressing a questio
 n of Bergelson from 1996.\n
LOCATION:https://researchseminars.org/talk/NTWebSeminar/303/
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