First order rigidity of high-rank arithmetic groups
1,634 views · Published 29 January 2018 · 56:07 · Indexed 22 September 2026
Channel: Institut Henri Poincaré · 2018 · Science & Technology
By Alex Lubotzky (Hebrew U.) Abstract: 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 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.
More from this channel
-
54:09
Le nombre de rotation et ses avatars
-
1:30:06
12e Forum des jeunes mathématiciennes - Femmes et Mathématiques
-
1:16:49
Michel Hénon Numerical studies of hamiltonian systems and application to galactic potentials
-
32:09
Hénon's generating solutions and the structure of periodic orbits families...
-
38:22
Michel Hénon et les amas globulaires
-
48:30
Gilbert Levitt - Vertex finiteness for relatively hyperbolic groups
-
20:25
1 - Kick-off afternoon : introduction and welcoming word by Cédric Villani
-
1:04:53
9 - Lectures : Jean-Yves Girard 2/3, Qu'est-ce qu'une question ? (le format)