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Kobi Peterzil (University of Haifa): Locally definable and approximate subgroups of semialgebraic groups

Donnerstag, 14.02.2019 11:00 im Raum SR 1D
Mathematik und Informatik

(w. E. Baro and P. Eleftheriou) A symmetric subset X of a group G is called a k-approximate subgroup of G if k-many group-translates of X cover XX. Given a natural number n, we let X(n)=XX^{-1}.....XX^{-1} (n times), and ask: are there n and k such that X(n) is a k-approximate subgroup of G? We do not know the answer when G=(R^n,+) and X is an *arbitrary* smooth curve. We give a positive answer to the above question when G is an abelian semialgebraic group over some real closed field and X is a semialgebraic subset of G (more generally when X is definable in certain o-minimal expansions of R). In these cases, we obtain uniform bounds for k and n in terms of X. I will describe the above result and the connection to a still-open problem about definably generated abelian groups in o-minimal structures.



Angelegt am Donnerstag, 31.01.2019 09:15 von pfeifer
Geändert am Montag, 04.02.2019 09:23 von pfeifer
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