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{\Large Department of Mathematics, BGU}
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{\Huge Colloquium}\\[0.2\baselineskip]
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\textbf{On} \emph{Tuesday, November 21, 2017}
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\textbf{At} \emph{14:30 -- 15:30}
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\textbf{In} \emph{Math -101}
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{\large\scshape Alex Lubotzky
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(Hebrew University)
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will talk about
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{\Large\bfseries First order rigidity of high-rank arithmetic groups\par}
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\textsc{Abstract:}
The family of high rank arithmetic groups is class of groups which is playing an important role in various areas of mathematics. It includes SL(n,Z), for n\textgreater{}2 , SL(n, Z{[}1/p{]} ) for n\textgreater{}1, their finite index subgroups and many more. A number of remarkable results about them have been proven including; Mostow rigidity, Margulis Super rigidity and the Quasi-isometric rigidity. We will talk about a new type of rigidity : ``first order rigidity''. Namely if D is such a non-uniform characteristic zero arithmetic group and E a finitely generated group which is elementary equivalent to it ( i.e., the same first order theory in the sense of model theory) then E is isomorphic to D. This stands in contrast with Zlil Sela's remarkable work which implies that the free groups, surface groups and hyperbolic groups ( many of which are low-rank arithmetic groups) have many non isomorphic finitely generated groups which are elementary equivalent to them.
Joint work with Nir Avni and Chen Meiri.
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