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March 18,Hillel Furstenberg（Hillel Furstenberg）andGregory Margulis(Gregory Margulis) won the 2020Abel Prize——One of the highest honors in mathematics, in recognition of theirgroup theory、number theoryandCombinatoricspioneering use inProbabilitywithdynamicsmethod.
they userandom walk technique(random walk techniques) to study the structure of a linear group by taking the product of randomly selected matrices to describe how the result will grow and what this growth means for the structure of the group. The two bridged the gaps between different fields of mathematics and solved problems that seemed out of reach.
○ Both Furstenberg (left) and Margulis (right) suffered unfair treatment because of their Jewish identities. Furstenberg was born in Berlin in 1935. When he was 4 years old, he fled the Nazis with his family and settled in New York. He later moved to Israel and taught at the Hebrew University of Jerusalem until his retirement in 2003. Margulis was born in Moscow in 1946 and was a victim of the anti-Semitic system. His Jewish identity prevented him from going abroad to receive the Fields Medal in 1978; he later immigrated to the United States and is still engaged in mathematics research at Yale University. | Image credit: Yosef Adest/Dan Renzetti
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If you hide some treats in the garden for your dog to find, he will immediately start searching with his sensitive nose. Its sniffing trail looks to be quiterandomApparently, this dog doesn't like a systematic way of searching. But anyway, after a short while, it found the "trophy". A dog's instincts give it the innate knowledge of how to search in constantly changing directions in a random manner.
In mathematics, this search behavior of dogs can be summarized and classified asrandom walkin the concept. Random walk isprobability theoryA core branch of , which describes a path consisting of a series of random steps in mathematical space.
In our lives, many physical systems are described by this kind of random walk, such as the behavior of gas molecules, the rise and fall of the stock market, the statistical properties of genetic drift, and the firing of neurons in the brain. But a random walk can also be seen as a tool for exploring mathematical objects, like a dog trying to understand a garden.
However, Furstenberg and Margulis's random walk was not used to find the prize buried in the garden;FigureorgroupOn, they tried to use random walks to reveal the secrets of these mathematical objects.
3 · Sophie Lie Lie group Abel Galois unboundedness Traversal recursion Henri Poincaré 4 · Furstenberg boundary disjointness
Super rigid
normal subgroup theorem
Oppenheim conjecture
integral solution
Ergodic Theory
Andre Semeredi
\Turing Award/
On the same day, ACM announced the "Nobel Prize in Computing"Turing AwardThe winners are:Edwin CatmullandPatrick Hanrahan, in recognition of their fundamental contributions to 3D computer graphics and the revolutionary impact of these technologies on the application of computer imaging in film production and other aspects. Their work fundamentally impacted the field of computer graphics and had a revolutionary impact on film production.
Deborah Coleman / Pixar; Andrew Brodhead / Stanford University
Machine-translated from the Chinese original 用随机阐释确定 | 2020年阿贝尔奖 (published 2020-03-20). WeChat original ↗