Dipartimento di Matematica, Aula Riunioni.<\/p>\n
Given an abelian group $G$, a corner is a a subset of pairs of the form $(x,y),(x+g,y),(x,y+g)$ with $g$ non trivial. Ajtai and Szemer\u00e9di proved that, asymptotically for finite abelian groups, every dense subset $S$ of $G\u00d7G$ contains an corner. Shkredov gave a quantitative lower bound on the density of the subset $S$. In this talk, we will explain how model-theoretic conditions on the subset $S$, such as local stability, will imply the existence of corners and of other configurations for (pseudo-)finite abelian groups. This is joint work with D. Palacin (Madrid) and J. Wolf (Cambridge).
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Further information is available on the event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":" Given an abelian group $G$, a corner is a a subset of pairs of the form $(x,y),(x+g,y),(x,y+g)$ with $g$ non trivial. Ajtai and Szemer\u00e9di proved that, asymptotically for finite abelian groups, every dense subset $S$ of $G\u00d7G$ contains an corner.…<\/p>\n