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.

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.

## Date:

Tue, 26/06/2018 - 10:00 to 11:00

## Location:

Manchester House, Lecture Hall 2