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A. Lubotzky: First order rigidity of high-rank arithmetic groups

Mittwoch, 07.06.2017 14:30 im Raum SR 1D
Mathematik und Informatik

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>2 , SL(n, Z[1/p] ) for n>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 whose 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.



Angelegt am Dienstag, 06.06.2017 13:34 von lammers
Geändert am Dienstag, 06.06.2017 13:34 von lammers
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