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SUMMARY:Roth numbers: Upper\, lower bounds\, and related constructions - Y
 aël Dillies (University of Cambridge)
DTSTART:20230622T160000Z
DTEND:20230622T170000Z
UID:TALK202663@talks.cam.ac.uk
CONTACT:Angeliki Koutsoukou-Argyraki
DESCRIPTION:The maximum number of integers between 1 and n that one can ta
 ke without creating an arithmetic progression of length 3 might sound like
  a trivial concern. It is in fact a foundational problem in additive combi
 natorics.\n\nI will explain how we formalised Roth's upper bound\, Behrend
 's lower bound and derived the proof to the Ruzsa-Szemerédi. Finally\, I 
 will outline how we will attack the brand new upper bound of Kelley and Me
 ka.\n\nAll work joint with Bhavik Mehta.
LOCATION:MR20 Centre for Mathematical Sciences
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