Grigori 'Grisha' Yakovlevich Perelman (Russian: Григорий Яковлевич Перельман) is a Russian mathematician who is an expert on Ricci flow. It is thought that he has proven the Poincaré conjecture, a major open problem in mathematics.
Perelman got his Ph.D. at the Mathematics & Mechanics Faculty of the St. Petersburg State University. Then he began working at the Petersburg Department of Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, Russia. His advisors at the Steklov Institute were Aleksandr Danilovich Aleksandrov and Yuri Dmitrievich Burago .
In the late 80s and early 90s, Perelman worked at various universities in United States. He returned to Russia in 1995 or 1996. Since then, has been quietly working at the Steklov Institute. Until the fall of 2002, Perelman was best known for his work in comparison geometry , proving several notable results, such as the Soul Conjecture.
In November 2002, he e-published on the arXiv website the first of a series of papers purporting to prove Thurston's Geometrization Conjecture, a result that includes the Poincaré conjecture as a particular case. The Poincaré conjecture, proposed by French mathematician Henri Poincaré in 1904, is considered, by many, to be the most famous problem in topology. Many mathematicians have unsuccessfully tried to prove it and Clay Mathematics Institute has announced $1 million dollar reward for its proof.
Perelman's plan of attack lies in modifying Richard Hamilton 's program for geometrization through Ricci flow. Compared to the more direct, topological programs (notably the differing approaches of W.P. Thurston, J.W. Cannon, and D. Gabai), this Ricci flow approach appears particularly promising at this stage.
As of September 2004, Perelman's work is still under review by the mathematical community. He has given a sequence of lectures at leading universities, explaining parts of the proof that have been e-published on the arXiv. The known parts are considered to be very plausible but not all details have been verified yet.
There is speculation whether he will receive the $1 million prize if the proof continues unchallenged. He turned down a prize from the European Mathematical Society in the early 1990s, is said to be "very unmaterialistic", and has not shown interest in publication of the proof in a peer-reviewed mathematics journal, as the current rules for the prize require. On the other hand, the scrutiny the on-line publication has already elicited is said to be well beyond that of pre-publication peer review, and the grantor has explicitly stated that its board may change the requirements.
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- Notes and commentary on Perelman's Ricci flow papers
- Perelman's papers published on arXiv.org
- Mathematics & Mechanics Faculty of St. Petersburg State University
- Petersburg Department of Steklov Institute of Mathematics
- Staff listing for Perelman at Petersburg Department of Steklov Institute of Mathematics