The Norwegian Academy of Science and Arts announced on March 18th that it would award one of the most prestigious prizes in mathematics, the 2020 Abel Prize, to Israeli mathematician Hillel Furstenberg and Russian-American mathematician Gregory Margulies. Margulis), in recognition of their “groundbreaking use of probability and kinetic methods in group theory, number theory, and combination theory”.
(Original title: The Abel Prize for Mathematics’ top prize is awarded to Scientists, and the award ceremony is postponed until the following year)
Journalist Zhang Wei
Hiller Furstenberg and Gregory Margulies
Named after the 19th-century Norwegian mathematician Niels Henrik Abel, the Abel Prize was established in 2003. The two winners will share 7.5 million Norwegian kroner, or about $834,000.
The Norwegian Academy of Science and Arts intends to postpone the awards ceremony, which usually takes place in Oslo in June, due to the current outbreak of the new coronavirus. The Academy decided to present the awards to the 2020 and 2021 winners at the 2021 awards ceremony.
The Norwegian Academy of Science and Arts said in a statement that Forstenberg and Margulies found an surprising and rich link between group theory, probability theory, number theory, combination theory and graph theory. “Their work has created a school that has had a profound impact on many areas of mathematics and application. “
The same day’s Nature news review said the two men bridged the gap between different fields of mathematics and solved problems that seemed out of reach.
Both Forstenberg and Margulies were discriminated against because of their Jewish backgrounds, According to Nature News.
Hillel Furstenberg was born in Berlin, Germany, in 1935 and taught at the Hebrew University of Israel before retiring. At the age of four, his family settled in New York to escape Nazi persecution. Forstenberg later moved to Israel and went to the Hebrew University of Jerusalem in 1965 until his retirement in 2003.
Gregory Margulies was born in Moscow in 1946, and his Jewish status prevented him from going abroad in 1978 to receive another major prize in mathematics. Margulies later immigrated to the United States and remains active at Yale University.
Upon learning of the award, Furstenberg said his reaction was “completely unconvinced,” according to Nature News. “I know the prestige of the Abel Award, and I know the list of previous winners,” “I just think they’re at some level, and I’m not at that level.” He said he didn’t foresee the impact of his ideas years ago. “Like any mathematician, I followed my nose looking for things that looked interesting. Margulies said he was honored to receive such recognition from the mathematical community.
A central branch of probability theory is random walking research, for example, when a tourist explores an unknown city, by tossing a coin to determine the route of left or right at each intersection. Hillel Furstenberg and Gregory Margulies invented similar random walk techniques to study the structure of linear groups, using the product of randomly selected matrices to describe how the results would grow and what that growth would mean for the structure of the group.
According to the Norwegian Academy of Science and Arts, Forstenberg introduced the concept of disjointing of Forstenberg boundaries and traversal systems, while Margulies proposed the concept of ultra-rigidity and “regular sub-group theorem”. In 1977, Forstenberg used the traversal theory to give new proof of the Szemer?di’s theorem. Margulies also proves the decades-old Oppenheimer hypothesis.
“The influence of Forstenberg and Margulies goes far beyond their results and original areas,” the Norwegian Academy of Science and Arts said. They were pioneered by mathematicians in many fields, from Li quns, discrete groups and random matrices to computer science and graphtheory. “
The 2019 Abel Prize winner is Karen Keskulla Uffbeck, emeritus professor at the University of Texas at Austin, the first female winner of the award.