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SUMMARY:Stability and Roth's Theorem on 3-AP's
DTSTART:20240516T123000Z
DTEND:20240516T133000Z
DTSTAMP:20240530T154600Z
UID:indico-event-276@events.dm.unipi.it
DESCRIPTION:Speakers: Daniel PalalcĂn (Universidad Complutense de Madrid)
\n\nRoth's theorem on arithmetic progression states that a subset A of the
natural numbers of positive upper density contains an arithmetic progress
ion of length $3$\, that is\, the equation $x+z=2y$ has a solution in $A$.
Likewise\, one can consider a similar statement for finite groups\, by co
nsidering the normalized counting measure\, and ask whether the equation $
x\\cdot z=y\\cdot y$ has a solution in a set of a fixed density. In this t
alk\, I will explain how to use the model-theoretic notion of connected co
mponent\, as well as of stability\, to obtain Roth-like statements for sui
table definably amenable groups. This is joint work with A. Martin-Pizarro
(Freiburg).\n\nhttps://events.dm.unipi.it/event/276/
LOCATION:Aula Riunioni (Dipartimento di Matematica)
URL:https://events.dm.unipi.it/event/276/
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