# Registration for the online Abel Prize celebrations

The registration for the Abel week 25th and 26th of May is now open. All the events will be held online: The Award Ceremony, the Abel reception, and the Abel lectures. The events will honour both the 2020-winners, Hillel Furstenberg and Gregory Margulis, and the 2021-winners, Avi Wigderson and László́ Lovász.

## Click here to register for the online events

## The Abel Prize award ceremony

May 25th | 3pm CEST

The ceremony will be broadcasted from the University Aula in Oslo. Haddy N'jie, Norwegian singer, songwriter, writer and journalist will be the master of ceremonies.

^{Haddy N'jie leads the ceremony from the University Aula}

### Highlights

- The Abel Committee’s Citation by Professor Hans Munthe-Kaas, Chair of the Abel Committee
- Awarding of the Abel Prize
- Acceptance speech by the four Abel laureates
- Closing speech by Professor Hans Petter Graver, President of The Norwegian Academy of Science and Letters
- Musical performances by Sonoro Quartet, Emma Martine Lam Olsen og Joakim Rřbergshagen.

## The Abel reception

May 25th | 6pm CEST

**Programme**

Speeches by:

- Henrik Asheim, Minister of Research and Higher Education, Norway
- Hans Petter Graver, President of The Norwegian Academy of Science and Letters
- Ruth Charney, President of American Mathematical Society
- Carlos Kenig, President of International Mathematical Union

- Minister for Innovation and Technology in Hungary, László Palkovics
- Acting Director of the White House Office of Science and Technology Policy, Kei Koizumi

Israeli Ambassador to Norway, Alon Roth

- Interview collage of the laureates
- Live music by Need Strings

## The Abel lectures

May 26th | 3pm - 8pm CEST

### Programme

3pm - 5pm CEST**Hillel Furstenberg**: Random walks in non-euclidean space and the Poisson boundary of a group**Gregory Margulis**: Arithmeticity of discrete subgroups and related topics

6pm - 8pm CEST**László Lovász**: Continuous limits of finite structures**Avi Wigderson**: The Value of Errors in Proofs

There will be opportunities for questions from the audience.

### Abstracts

**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**Download presentation (pdf)

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.

**László Lovász - Continuous limits of finite structures**

The idea that a sequence of larger and larger finite structures tends to a limit has been around for quite a while, going back (at least) to John von Neumann's "continuous geometries".

After a brief survey of the history of such constructions, we turn to limits of graph sequences; this theory was worked out for dense graphs and bounded-degree graphs more than a decade ago. The "intermediate" cases (for example, the sequence of hypercubes, or incidence graphs of finite geometries) represent much more difficult problems, and only partial results can be reported. Perhaps surprisingly, the limit objects, whenever known, are best described as Markov chains on measurable spaces.

Why are we making such efforts to construct such limit objects? The talk will show a couple of examples of interesting graph-theoretic problems where graph limits are needed even for the precise statement of the problem, or as the starting point of the solution.

**Avi Wigderson - The Value of Errors in Proofs**

A few months ago, a group of theoretical computer scientists posted a paper on the Arxiv with the strange-looking title "MIP* = RE", surprising and impacting not only complexity theory but also some areas of math and physics. Specifically, it resolved, in the negative, the "Connes' embedding conjecture" in the area of von-Neumann algebras, and the "Tsirelson problem" in quantum information theory. It further connects Turing's seminal 1936 paper which defined algorithms to Einstein's 1935 paper with Podolsky and Rosen which challenged quantum mechanics. You can find the paper here: https://arxiv.org/abs/2001.04383

As it happens, both acronyms MIP* and RE represent proof systems, of a very different nature. To explain them, we'll take a meandering journey through the classical and modern definitions of proof. I hope to explain how the methodology of computational complexity theory, especially modeling and classification (of both problems and proofs) by algorithmic efficiency, naturally leads to the genaration of new such notions and results (and more acronyms, like NP). A special focus will be on notions of proof which allow interaction, randomness, and errors, and their surprising power and magical properties.

The talk will be non-technical, and requires no special background.

### The Abel Prize celebrations - live

### Watch the Abel Prize celebrations live

### Lovász and Wigderson to share the Abel Prize

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2021 to László Lovász of Alfréd Rényi Institute of Mathematics (ELKH, MTA Institute of Excellence) and Eötvös Loránd University in Budapest, Hungary, and Avi Wigderson of the Institute for Advanced Study, Princeton, USA,

“for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics”

### Announcement of the next Abel Prize laureate

The Abel Prize laureate for 2021 will be announced Wednesday March 17th at 12:00 (UTC/GMT+1).** **

### Isadore M. Singer, Abelprize laureate, dies at 96

Isadore M. Singer was the recipient together with Sir Michael Atiyah of the Abel Prize in 2004. They received the prize for their discovery and proof of the index theorem, one of the most significant discoveries in 20th century mathematics.

(12.02.2021) More### Sir Vaughan F.R. Jones, outstanding mathematician and incoming member of the Abel committee, has passed away

(11.09.2020) More### The Honouring of the 2020 Abel Prize Laureates

All events in connection to the Abel Prize Week in May are cancelled due to the Corona pandemic. The 2020 Abel Prize Laureates Hillel Furstenberg and Gregory Margulis will be honoured, together with the Abel Prize Laureate(s) of 2021 during next year’s Abel Prize Ceremony, May 25 2021.