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Logic Seminar - Alex Lubotzky - "First order rigidity of high-rank arithmetic groups" | Einstein Institute of Mathematics

Logic Seminar - Alex Lubotzky - "First order rigidity of high-rank arithmetic groups"

Date: 
Wed, 10/01/201811:00-13:00
Location: 
Ross 63
The family of high rank arithmetic groups is a class of groups 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 G is such a non-uniform characteristic zero arithmetic group and H a finitely generated group which is elementary equivalent to it then H is isomorphic to G. This stands in contrast with Zlil Sela's seminal 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.