The Abel lectures: Hillel Furstenberg and Gregory Margulis

0:30 Welcome by Hans Petter Graver, President of the Norwegian Academy of Science Letters
01:37 Introduction by Hans Munthe-Kaas, Chair of the Abel Prize Committee
04:16 Hillel Furstenberg: Random walks in non-euclidean space and the Poisson boundary of a group
58:40 Questions and answers
1:03:55 Introduction by Hans Munthe-Kaas, Chair of the Abel Prize Committee
1:05.39 Gregory Margulis: Arithmeticity of discrete subgroups and related topics
1:55:07 Questions and answers
Hillel Furstenberg - Group boundaries: between harmonic functions and random walks
The classical theory of harmonic functions and their "boundary values", seen in a broad setting, leads to a notion of boundaries for general locally compact groups. It is useful because it can be made explicit for semi-simple Lie groups.Under certain conditions, the boundary of a group and a lattice subgroup coincide, so this notion is useful in rigidity questions.
It also plays a role in studying the asymptotic behavior of random walks on non-commutative groups, and as an application, helps establish a "qualitative" law of large numbers for products of matrices.
Gregory Margulis - Arithmeticity of discrete subgroups and related topics
In late 1950s, A.Selberg conjectured that, with few exceptions, all discrete co-compact (or, more generally with finite covolume) subgroups in semisimple Lie groups should be of arithmetic nature. He also obtained some partial results in this direction. I will start with a short description of this work by Selberg. The arithmeticity conjecture is related to the rigidity phenomenon in the theory of discrete subgroups of Lie groups.
Eventually the arithmeticity conjecture was proved in most cases using various approaches, most notably so called superrigidity theorem. The proof of the superrigidity theorem is bases on applications of methods from ergodic theory/probability.
The talk will be non-technical, and requires no special background.

[@tusharhalder64]

Hillel 🥰 this motivates young math students like us 🥰

[@dunyanneniyisi6450]

Can you add subtitles?

[@davidwilkie9551]

Could the objective of the Math-Phys-Chem and Geometrical Sciencing of be refined to reiterate the Law, as it is applied to Human heirachical Affairs, again?