Abel Prize 2020: Furstenberg and Margulis

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2020 to Hillel Furstenberg (left in the photo), Hebrew University of Jerusalem, Israel​ and Gregory Margulis (right in the photo), Yale University, New Haven, CT, USA,

for pioneering the use of methods from probability and dynamics in group theory, number theory and combinatorics.

---

Hillel Furstenberg and Gregory Margulis invented random walk techniques to investigate mathematical objects such as groups and graphs, and in so doing introduced probabilistic methods to solve many open problems in group theory, number theory, combinatorics and graph theory. A random walk is a path consisting of a succession of random steps, and the study of random walks is a central branch of probability theory.

The works of Furstenberg and Margulis have demonstrated the effectiveness of crossing boundaries between separate mathematical disciplines and brought down the traditional wall between pure and applied mathematics

says Hans Munthe-Kaas, chair of the Abel committee. He continues:

Furstenberg and Margulis stunned the mathematical world by their ingenious use of probabilistic methods and random walks to solve deep problems in diverse areas of mathematics. This has opened up a wealth of new results, such as the existence of long arithmetic progressions of prime numbers, understanding the structure of lattices in Lie groups, and the construction of expander graphs with applications to communication technology and computer science, to mention a few.

---

Due to the corona pandemic there will not be a physical Laureate ceremony on May 19 this year. The honoring of the Abel Prize Laureates will be announced later.

---

press release

Dyson sphere

A heartfelt tribute to Freeman Dyson

---

(...) Dyson is too modest.
Richard Carrigan⁽⁸⁾

The search for extraterrestrial life has, as I already written, some illustrious founding fathers: Enrico Fermi and his paradox; Giuseppe Cocconi and Philip Morrison and their 1959 proposal to use radio astronomy to search for extraterrestrial signals of intelligent origin⁽¹⁾; Frank Drake with his famous equation, and therefore with the Ozma project⁽²⁾, so called for the queen of the imaginary land of Oz, a very distant place, difficult to reach and populated by exotic beings, a kind of proto-SETI, project that Drake helped to found and launch.
Another important contribution to the quest of intelligent signal in the universe come from Freeman Dyson^{(3, 8)}:

If extraterrestrial intelligent beings exist and have reached a high level of technical development, one by-product of their energy metabolism is likely to be the large-scale conversion of starlight into far-infrared radiation. It is proposed that a search for sources of infrared radiation should accompany the recently initiated search for interstellar radio communications.⁽³⁾

Dyson, taking our solar system as a model, observed how the mass of Jupiter, if distributed with spherical symmetry on a double orbit compared to that of the Earth, would have been 2 tons per square meter thick:

A shell of this thickness could be made comfortably habitable, and could contain all the machinery required for exploiting the solar radiation falling onto it from the inside⁽³⁾