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SUMMARY:The slice rank polynomial method and its limitations
DTSTART:20230208T160000
DTEND:20230208T170000
DTSTAMP:20260407T112528Z
UID:e04ac63feccbb63531443169702d432cfa5cef05852749bebeb8f2d1
CATEGORIES:Conferences - Seminars
DESCRIPTION:Lisa Sauermann\, MIT \nSeminar in Mathematics\nAbstract: The s
 lice rank polynomial method is a fairly new polynomial method\, developed 
 by Tao (building on work of Croot-Lev-Pach and Ellenberg-Gijswijt) in the 
 context of the famous cap-set problem. This problem asks about the maximum
  possible size of a subset of F_3^n not containing a three-term arithmetic
  progression\, and Ellenberg-Gijswijt proved that any such subset has size
  at most 2.756^n. The slice rank polynomial method also lead to progress o
 n various other problems in extremal combinatorics and additive number the
 ory. However\, the method is not very flexible\, and even small changes to
  the setting can bring the method to fail. This talk discusses several pro
 blems where the slice rank polynomial method can be combined with combinat
 orial and probabilistic tools in order to overcome some of its limitations
 . Specifically\, the talk discusses results on the Erdös-Ginzburg-Ziv pro
 blem in discrete geometry\, on extremal questions in additive number theor
 y about subsets of F_p^n without distinct-variable solutions to certain (s
 ystems of) linear equations\, and on bounds for arithmetic removal lemmas 
 (which are closely connected to property testing problems in theoretical c
 omputer science).\n\n 
LOCATION:https://epfl.zoom.us/j/68693543359
STATUS:CONFIRMED
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