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83-699: The Society seeks to serve all kinds of mathematicians in universities, research institutes and other forms of higher education. Its aims are to The EMS is itself an Affiliate Member of the International Mathematical Union and an Associate Member of the International Council for Industrial and Applied Mathematics . The precursor to the EMS, the European Mathematical Council was founded in 1978 at

166-665: A Fields Medal for his work on the Ricci flow. However, Perelman declined to accept the prize. Sir John Ball , president of the International Mathematical Union , approached Perelman in Saint Petersburg in June 2006 to persuade him to accept the prize. After 10 hours of attempted persuasion over two days, Ball gave up. Two weeks later, Perelman summed up the conversation as follows: " He proposed to me three alternatives: accept and come; accept and don't come, and we will send you

249-421: A Ricci flow with surgery in three dimensions, systematically excising singular regions as they develop. As an immediate corollary of his construction, Perelman resolved a major conjecture on the topological classification in three dimensions of closed manifolds which admit metrics of positive scalar curvature . His third preprint (or alternatively Colding and Minicozzi's work) showed that on any space satisfying

332-467: A closed three-dimensional manifold has the property that any loop can be contracted into a point, then it must be topologically equivalent to a 3-sphere. Stephen Smale proved a high-dimensional analogue of Poincaré's conjecture in 1961, and Michael Freedman proved the four-dimensional version in 1982. Despite their work, the case of three-dimensional spaces remained completely unresolved. Moreover, Smale and Freedman's methods have had no impact on

415-407: A Riemannian metric, in certain geometric settings. As a byproduct, he was able to prove some new and striking theorems in the field of Riemannian geometry . Despite formal similarities, Hamilton's equations are significantly more complex and nonlinear than the heat equation, and it is impossible that such uniformization is achieved without contextual assumptions. In completely general settings, it

498-410: A compact nonnegatively curved submanifold, called a soul , whose normal bundle is diffeomorphic to the original space. From the perspective of homotopy theory , this says in particular that every complete Riemannian metric of nonnegative sectional curvature may be taken to be closed . Cheeger and Gromoll conjectured that if the curvature is strictly positive somewhere, then the soul can be taken to be

581-409: A consequence, Hamilton's compactness and the corresponding existence of subsequential limits could be applied somewhat freely. The "canonical neighborhoods theorem" is the second main result of Perelman's first preprint. In this theorem, Perelman achieved the quantitative understanding of singularities of three-dimensional Ricci flow which had eluded Hamilton. Roughly speaking, Perelman showed that on

664-462: A followup unpublished paper, Perelman proved his "stability theorem," asserting that in the collection of all Alexandrov spaces with a fixed curvature bound, all elements of any sufficiently small metric ball around a compact space are mutually homeomorphic . Vitali Kapovitch, who described Perelman's article as being "very hard to read," later wrote a detailed version of Perelman's proof, making use of some further simplifications. Perelman developed

747-606: A high priority for the IMU and a significant percentage of its budget, including grants received from individuals, mathematical societies, foundations, and funding agencies, is spent on activities for developing countries. Since 2011 this has been coordinated by the Commission for Developing Countries (CDC). The Committee for Women in Mathematics (CWM) is concerned with issues related to women in mathematics worldwide. It organizes

830-400: A manifold. The heat equation, such as when applied in the sciences to physical phenomena such as temperature , models how concentrations of extreme temperatures will spread out until a uniform temperature is achieved throughout an object. In three seminal articles published in the 1980s, Hamilton proved that his equation achieved analogous phenomena, spreading extreme curvatures and uniformizing

913-528: A microscopic level, every singularity looks either like a cylinder collapsing to its axis, or a sphere collapsing to its center. Perelman's proof of his canonical neighborhoods theorem is a highly technical achievement, based upon extensive arguments by contradiction in which Hamilton's compactness theorem (as facilitated by Perelman's noncollapsing theorem) is applied to construct self-contradictory manifolds. Other results in Perelman's first preprint include

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996-432: A new theorem characterizing manifolds in which collapsing is only assumed on a local level. In his preprint, he said the proof of his theorem would be established in another paper, but he did not then release any further details. Proofs were later published by Takashi Shioya and Takao Yamaguchi, John Morgan and Gang Tian , Jianguo Cao and Jian Ge, and Bruce Kleiner and John Lott . Perelman's preprints quickly gained

1079-549: A number of textbooks and expository articles. " Perelman's proofs are concise and, at times, sketchy. The purpose of these notes is to provide the details that are missing in [Perelman's first two preprints]... Regarding the proofs, [Perelman's papers] contain some incorrect statements and incomplete arguments, which we have attempted to point out to the reader. (Some of the mistakes in [Perelman's first paper] were corrected in [Perelman's second paper].) We did not find any serious problems, meaning problems that cannot be corrected using

1162-511: A pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit." (''The New Yorker'' authors explained Perelman's reference to "some ugly thing" as "a fuss" on Perelman's part about the ethical breaches he perceived.) " It was unclear whether along with his resignation from Steklov and subsequent seclusion Perelman stopped his mathematics research. Yakov Eliashberg , another Russian mathematician, said that in 2007 Perelman confided to him that he

1245-678: A report in 2008, Mathematics in Africa: Challenges and Opportunities , on the current state of mathematics in Africa and on opportunities for new initiatives to support mathematical development. In 2014, the IMU's Commission for Developing Countries CDC released an update of the report. Additionally, reports about Mathematics in Latin America and the Caribbean and South East Asia . were published. In July 2014 IMU released

1328-4542: A researcher or group of researchers '"for highly original and influential work in the field of history of mathematics that enhances our understanding of either the development of mathematics or a particular mathematical subject in any period and in any geographical region". The following are the awardees so far, (a symbol denotes mathematicians who later earned a Fields Medal ). EMS Prizes: Richard Borcherds (UK) – Jens Franke (Germany) – Alexander Goncharov (Russia) – Maxim Kontsevich (Russia) – François Labourie (France) – Tomasz Łuczak (Poland) – Stefan Müller (Germany) – Vladimír Šverák (Czechoslovakia) – Gábor Tardos (Hungary) – Claire Voisin (France) EMS Prizes: Alexis Bonnet (France) – Timothy Gowers (UK) – Annette Huber-Klawitter (Germany) – Aise Johan de Jong (Netherlands) – Dmitry Kramkov (Russia) – Jiří Matoušek (Czech Republic) – Loïc Merel (France) – Grigori Perelman (Russia), declined – Ricardo Pérez-Marco (Spain/France) – Leonid Polterovich (Russia/Israel) EMS Prizes: Semyon Alesker (Israel) – Raphaël Cerf (France) – Dennis Gaitsgory (Moldova) – Emmanuel Grenier (France) – Dominic Joyce (UK) – Vincent Lafforgue (France) – Michael McQuillan (UK) – Stefan Nemirovski (Russia) – Paul Seidel (UK/Italy) – Wendelin Werner (France) Felix Klein Prize: David C. Dobson (USA) EMS Prizes: Franck Barthe (France) – Stefano Bianchini (Italy) – Paul Biran (Israel) – Elon Lindenstrauss (Israel) – Andrei Okounkov (Russia) – Sylvia Serfaty (France) – Stanislav Smirnov (Russia) – Xavier Tolsa (Spain) – Warwick Tucker (Australia/Sweden) – Otmar Venjakob  [ de ] (Germany) Felix Klein Prize: Not Awarded EMS Prizes: Artur Avila (Brazil) – Alexei Borodin (Russia) – Ben J. Green (UK) – Olga Holtz (Russia) – Boáz Klartag (Israel) – Alexander Kuznetsov (Russia) – Assaf Naor (USA/Israel) – Laure Saint-Raymond (France) – Agata Smoktunowicz (Poland) – Cédric Villani (France) Felix Klein Prize: Josselin Garnier (France) EMS Prizes: Simon Brendle (Germany) - Emmanuel Breuillard (France) - Alessio Figalli (Italy) - Adrian Ioana (Romania) - Mathieu Lewin (France) - Ciprian Manolescu (Romania) - Grégory Miermont (France) - Sophie Morel (France) - Tom Sanders (UK) - Corinna Ulcigrai (Italy) - Felix Klein Prize: Emmanuel Trélat (France) Otto Neugebauer Prize: Jan P. Hogendijk (Netherlands) EMS Prizes: Sara Zahedi (Iran-Sweden) - Mark Braverman (Israel) - Vincent Calvez (France) - Guido de Philippis (Italy) - Peter Scholze (Germany) - Péter Varjú (Hungary) - Thomas Willwacher (Germany) - James Maynard (UK) - Hugo Duminil-Copin (France) - Geordie Williamson (Australia) Felix Klein Prize: Patrice Hauret (France) Otto Neugebauer Prize: Jeremy Gray (UK) EMS Prizes: Karim Adiprasito (Germany) - Ana Caraiani (Romania) - Alexander Efimov (Russia) - Simion Filip (Moldova) - Aleksandr Logunov (Russia) - Kaisa Matomäki (Finland) - Phan Thành Nam (Vietnam) - Joaquim Serra (Spain) - Jack Thorne (UK) - Maryna Viazovska (Ukraine) Felix Klein Prize: Arnulf Jentzen (Germany) Otto Neugebauer Prize: Karine Chemla (France) Source: EMS Prizes: Maria Colombo (Italy/Switzerland) - Cristiana De Filippis (Italy) - Jessica Fintzen (Germany) - Nina Holden (Norway/USA) - Tom Hutchcroft (UK/USA) - Jacek Jendrej (Poland/France) - Adam Kanigowski (Poland/USA) - Frederick Manners (UK/USA) - Richard Montgomery (UK) - Danylo Radchenko (Ukraine/France) Felix Klein Prize: Fabien Casenave (France) Otto Neugebauer Prize: Reinhard Siegmund-Schultze (Germany/Norway) Paul Lévy Prize in Probability Theory: Jeremy Quastel (Canada) The EMS

1411-425: A single point, and hence that the original space must be diffeomorphic to Euclidean space . In 1994, Perelman gave a short proof of Cheeger and Gromoll's conjecture by establishing that, under the condition of nonnegative sectional curvature, Sharafutdinov's retraction is a submersion . Perelman's theorem is significant in establishing a topological obstruction to deforming a nonnegatively curved metric to one which

1494-622: A third paper posted in July 2003, Perelman outlined an additional argument, sufficient for proving the Poincaré conjecture (but not the Thurston conjecture), the point being to avoid the most technical work in his second preprint. Perelman's first preprint contained two primary results, both to do with Ricci flow. The first, valid in any dimension, was based on a novel adaptation of Peter Li and Shing-Tung Yau 's differential Harnack inequalities to

1577-466: A three-dimensional version of his surgery techniques could be developed, and if a certain conjecture on the long-time behavior of Ricci flow could be established, then Thurston's conjecture would be resolved. This became known as the Hamilton program. In November 2002 and March 2003, Perelman posted two preprints to arXiv , in which he claimed to have outlined a proof of Thurston's conjecture. In

1660-615: A version of Morse theory on Alexandrov spaces. Despite the lack of smoothness in Alexandrov spaces, Perelman and Anton Petrunin were able to consider the gradient flow of certain functions, in unpublished work. They also introduced the notion of an "extremal subset" of Alexandrov spaces, and showed that the interiors of certain extremal subsets define a stratification of the space by topological manifolds . In further unpublished work, Perelman studied DC functions (difference of concave functions) on Alexandrov spaces and established that

1743-619: Is a Russian mathematician and geometer who is known for his contributions to the fields of geometric analysis , Riemannian geometry , and geometric topology . In 2005, Perelman resigned from his research post in Steklov Institute of Mathematics and in 2006 stated that he had quit professional mathematics, owing to feeling disappointed over the ethical standards in the field. He lives in seclusion in Saint Petersburg and has declined requests for interviews since 2006. In

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1826-815: Is administered by an executive committee (EC) which conducts the business of the Union. The EC consists of the President, two vice-presidents, the Secretary, six Members-at-Large, all elected for a term of four years, and the Past President. The EC is responsible for all policy matters and for tasks, such as choosing the members of the ICM Program Committee and various prize committees. Every two months IMU publishes an electronic newsletter, IMU-Net , that aims to improve communication between IMU and

1909-709: Is an international organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports the International Congress of Mathematicians (ICM). Its members are national mathematics organizations from more than 80 countries. The objectives of the International Mathematical Union are: promoting international cooperation in mathematics, supporting and assisting

1992-417: Is discussed by several leading mathematicians, including Mikhail Gromov , Ludwig Faddeev , Anatoly Vershik , Gang Tian , John Morgan and others, was released in 2011 under the title "Иноходец. Урок Перельмана" ("Maverick: Perelman's Lesson"). In April 2011, Aleksandr Zabrovsky, producer of "President-Film" studio, claimed to have held an interview with Perelman and agreed to shoot a film about him, under

2075-476: Is inevitable that "singularities" occur, meaning that curvature accumulates to infinite levels after a finite amount of "time" has elapsed. Following Shing-Tung Yau 's suggestion that a detailed understanding of these singularities could be topologically meaningful, and in particular that their locations might identify the spheres and tori in Thurston's conjecture , Hamilton began a systematic analysis. Throughout

2158-404: Is not people who break ethical standards who are regarded as aliens. It is people like me who are isolated." This, combined with the possibility of being awarded a Fields medal , led him to state that he had quit professional mathematics by 2006. He said: " As long as I was not conspicuous, I had a choice. Either to make some ugly thing or, if I didn't do this kind of thing, to be treated as

2241-590: Is periodically visiting his sister in Sweden, while living in Saint Petersburg and taking care of his elderly mother. Perelman has avoided journalists and other members of the media. Masha Gessen , author of a biography about Perelman, "Perfect Rigour: A Genius and the Mathematical Breakthrough of the Century ", was unable to meet him. A Russian documentary about Perelman in which his work

2324-516: Is positively curved, even at a single point. Some of Perelman's work dealt with the construction of various interesting Riemannian manifolds with positive Ricci curvature . He found Riemannian metrics on the connected sum of arbitrarily many complex projective planes with positive Ricci curvature, bounded diameter, and volume bounded away from zero. Also, he found an explicit complete metric on four-dimensional Euclidean space with positive Ricci curvature and Euclidean volume growth, and such that

2407-605: Is the sole shareholder of the publisher EMS Press that publishes over 25 academic journals , including: EMS Press has also published over 200 books in mathematics since 2003, in both print and digital formats. In addition, since 2021 it publishes the Magazine of the European Mathematical Society, often called EMS Magazine (ISSN 2747-7894, eISSN 2747-7908), formerly known as the Newsletter of

2490-539: Is why I don't want to have everybody looking at me. " Nevertheless, on 22 August 2006, at the International Congress of Mathematicians in Madrid , Perelman was offered the Fields Medal " for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow ". He did not attend the ceremony and the presenter informed the congress that Perelman declined to accept

2573-725: The Felix Klein Prize (endowed by the Institute for Industrial Mathematics in Kaiserslautern) has been awarded to "a young scientist or a small group of young scientists (normally under the age of 38) for using sophisticated methods to give an outstanding solution, which meets with the complete satisfaction of industry, to a concrete and difficult industrial problem." Since 2012, the Otto Neugebauer Prize (endowed by Springer Verlag ) has been awarded to

European Mathematical Society - Misplaced Pages Continue

2656-534: The Gottfried Wilhelm Leibniz Scientific Community , with about 120 scientists engaging in mathematical research applied to complex problems in industry and commerce. IMU has a close relationship to mathematics education through its International Commission on Mathematical Instruction (ICMI). This commission is organized similarly to IMU with its own Executive Committee and General Assembly. Developing countries are

2739-515: The International Congress of Mathematicians in Helsinki . This informal federation of mathematical societies was chaired by Sir Michael Atiyah . The European Mathematical Society was founded on 28 October 1990 in Mądralin near Warsaw , Poland , with Friedrich Hirzebruch as founding President. Initially, the EMS had 27 member societies. The first European Congress of Mathematics (ECM) was held at

2822-412: The Steklov Institute in Saint Petersburg in the summer of 1995 for a research-only position. In his undergraduate studies, Perelman dealt with issues in the field of convex geometry . His first published article studied the combinatorial structures arising from intersections of convex polyhedra . With I. V. Polikanova, he established a measure-theoretic formulation of Helly's theorem . In 1987,

2905-419: The Thurston geometrization conjecture , posited that given any closed three-dimensional manifold whatsoever, there is some collection of two-dimensional spheres and tori inside of the manifold which disconnect the space into separate pieces, each of which can be endowed with a uniform geometric structure. Thurston was able to prove his conjecture under some provisional assumptions. In John Morgan 's view, it

2988-762: The USSR Academy of Sciences , where his advisors were Aleksandr Aleksandrov and Yuri Burago . In the late 1980s and early 1990s, with a strong recommendation from the geometer Mikhail Gromov , Perelman obtained research positions at several universities in the United States. In 1991, Perelman won the Young Mathematician Prize of the Saint Petersburg Mathematical Society for his work on Aleksandrov's spaces of curvature bounded from below. In 1992, he

3071-415: The asymptotic cone is non-uniquely defined. The Poincaré conjecture , proposed by mathematician Henri Poincaré in 1904, was throughout the 20th century regarded as a key problem in topology . On the 3-sphere , defined as the set of points at unit length from the origin in four-dimensional Euclidean space , any loop can be contracted into a point. Poincaré suggested that a converse might be true: if

3154-624: The geometrization conjecture or the Poincaré conjecture . In April 2003, Perelman visited the Massachusetts Institute of Technology , Princeton University , Stony Brook University , Columbia University , and New York University to give short series of lectures on his work, and to clarify some details for experts in the relevant fields. In the years afterwards, three detailed expositions appeared, discussed below. Since then, various parts of Perelman's work have also appeared in

3237-512: The 1990s, he found a number of new technical results and methods, culminating in a 1997 publication constructing a "Ricci flow with surgery" for four-dimensional spaces . As an application of his construction, Hamilton was able to settle a four-dimensional curvature-based analogue of the Poincaré conjecture. Yau has identified this article as one of the most important in the field of geometric analysis , saying that with its publication it became clear that Ricci flow could be powerful enough to settle

3320-493: The 1990s, partly in collaboration with Yuri Burago , Mikhael Gromov , and Anton Petrunin, he made contributions to the study of Alexandrov spaces . In 1994, he proved the soul conjecture in Riemannian geometry, which had been an open problem for the previous 20 years. In 2002 and 2003, he developed new techniques in the analysis of Ricci flow , and proved the Poincaré conjecture and Thurston's geometrization conjecture ,

3403-520: The European Mathematical Society (ISSN 1027-488X), which was established in 1991. It features news and expositions of recent developments in mathematical research. It is quarterly and open access. The current editor-in-chief is Fernando da Costa (2020–) (succeeding Valentin Zagrebnov (2016–2020)). The Encyclopedia of Mathematics is also sponsored by the EMS. International Mathematical Union The International Mathematical Union ( IMU )

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3486-756: The IMU was also readmitted to the ICSU. The past president of the Union is Carlos Kenig (2019–2022). The current president is Hiraku Nakajima . At the 16th meeting of the IMU General Assembly in Bangalore, India , in August 2010, Berlin was chosen as the location of the permanent office of the IMU, which was opened on January 1, 2011, and is hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS), an institute of

3569-580: The IMU, in the quadrennial International Congress of Mathematicians (ICM), are deemed to be some of the highest distinctions in the mathematical world. These are: The IMU's members are Member Countries and each Member country is represented through an Adhering Organization, which may be its principal academy, a mathematical society, its research council or some other institution or association of institutions, or an appropriate agency of its government. A country starting to develop its mathematical culture and interested in building links with mathematicians all over

3652-506: The International Congress of Mathematicians and other international scientific meetings/conferences, acknowledging outstanding research contributions to mathematics through the awarding of scientific prizes, and encouraging and supporting other international mathematical activities, considered likely to contribute to the development of mathematical science in any of its aspects, whether pure, applied, or educational. The IMU

3735-2761: The International Mathematical Union from 1952 to the present: 1952–1954: [REDACTED] Marshall Harvey Stone (vice: [REDACTED] Émile Borel , [REDACTED] Erich Kamke ) 1955–1958: [REDACTED] Heinz Hopf (vice: [REDACTED] Arnaud Denjoy , [REDACTED] W. V. D. Hodge ) 1959–1962: [REDACTED] Rolf Nevanlinna (vice: [REDACTED] Pavel Alexandrov , [REDACTED] Marston Morse ) 1963–1966: [REDACTED] Georges de Rham (vice: [REDACTED] Henri Cartan , [REDACTED] Kazimierz Kuratowski ) 1967–1970: [REDACTED] Henri Cartan (vice: [REDACTED] Mikhail Lavrentyev , [REDACTED] Deane Montgomery ) 1971–1974: [REDACTED] K. S. Chandrasekharan (vice: [REDACTED] Abraham Adrian Albert , [REDACTED] Lev Pontryagin ) 1975–1978: [REDACTED] Deane Montgomery (vice: [REDACTED] J. W. S. Cassels , [REDACTED] Miron Nicolescu , [REDACTED] Gheorghe Vrânceanu ) 1979–1982: [REDACTED] Lennart Carleson (vice: [REDACTED] Masayoshi Nagata , [REDACTED] Yuri Vasilyevich Prokhorov ) 1983–1986: [REDACTED] Jürgen Moser (vice: [REDACTED] Ludvig Faddeev , [REDACTED] Jean-Pierre Serre ) 1987–1990: [REDACTED] Ludvig Faddeev (vice: [REDACTED] Walter Feit , [REDACTED] Lars Hörmander ) 1991–1994: [REDACTED] Jacques-Louis Lions (vice: [REDACTED] John H. Coates , [REDACTED] David Mumford ) 1995–1998: [REDACTED] David Mumford (vice: [REDACTED] Vladimir Arnold , [REDACTED] Albrecht Dold ) 1999–2002: [REDACTED] Jacob Palis (vice: [REDACTED] Simon Donaldson , [REDACTED] Shigefumi Mori ) 2003–2006: [REDACTED] John M. Ball (vice: [REDACTED] Jean-Michel Bismut , [REDACTED] Masaki Kashiwara ) 2007–2010: [REDACTED] László Lovász (vice: [REDACTED] Zhi-Ming Ma , [REDACTED] Claudio Procesi ) 2011–2014: [REDACTED] Ingrid Daubechies (vice: [REDACTED] Christiane Rousseau , [REDACTED] Marcelo Viana ) 2015–2018: [REDACTED] Shigefumi Mori (vice: [REDACTED] Alicia Dickenstein , [REDACTED] Vaughan Jones ) 2019–2022: [REDACTED] Carlos Kenig (vice: [REDACTED] Nalini Joshi , [REDACTED] Loyiso Nongxa ) 2023–2026: [REDACTED] Hiraku Nakajima (vice: [REDACTED] Ulrike Tillmann , [REDACTED] Tatiana Toro ) Grigori Perelman Grigori Yakovlevich Perelman (Russian: Григорий Яковлевич Перельман , IPA: [ɡrʲɪˈɡorʲɪj ˈjakəvlʲɪvʲɪtɕ pʲɪrʲɪlʲˈman] ; born 13 June 1966)

3818-729: The Mathematical Sciences), Ethics, European Solidarity, Meetings, Publications and Electronic Dissemination, Raising Public Awareness of Mathematics, Women in Mathematics. The EMS's rules are set down in its Statutes and Bylaws. The EMS is headquartered at the University of Helsinki . The European Congress of Mathematics (ECM) is held every four years under the Society's auspices, at which ten EMS Prizes are awarded to "recognize excellent contributions in Mathematics by young researchers not older than 35 years". Since 2000,

3901-581: The Millennium Prize in July 2010. He considered the decision of the Clay Institute unfair for not sharing the prize with Richard S. Hamilton , and stated that " the main reason is my disagreement with the organized mathematical community. I don't like their decisions, I consider them unjust. " The Clay Institute subsequently used Perelman's prize money to fund the "Poincaré Chair", a temporary position for young promising mathematicians at

3984-601: The Paris Institut Henri Poincaré . Perelman quit his job at the Steklov Institute in December 2005. His friends are said to have stated that he currently finds mathematics a painful topic to discuss; by 2010, some even said that he had entirely abandoned mathematics. Perelman is quoted in a 2006 article in The New Yorker saying that he was disappointed with the ethical standards of

4067-676: The Sorbonne and Panthéon-Sorbonne universities in Paris in 1992, and is now held every 4 years at different locations around Europe, organised by the EMS. ECM 2020 was postponed for a year due to the covid pandemic took place in 2021 in Portorož in Slovenia. The last ECM (2024) was in Seville . Source: The governing body of the EMS is its Council, which comprises delegates representing all of

4150-767: The Soviet team at the International Mathematical Olympiad hosted in Budapest, achieving a perfect score. He continued as a student of the School of Mathematics and Mechanics (the so-called "матмех" i.e. "math-mech") at Leningrad State University , without admission examinations, and enrolled at the university. After completing his PhD in 1990, Perelman began work at the Leningrad Department of Steklov Institute of Mathematics of

4233-405: The Thurston conjecture. The key of Hamilton's analysis was a quantitative understanding of how singularities occur in his four-dimensional setting; the most outstanding difficulty was the quantitative understanding of how singularities occur in three-dimensional settings. Although Hamilton was unable to resolve this issue, in 1999 he published work on Ricci flow in three dimensions, showing that if

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4316-839: The World Meeting for Women in Mathematics ( ( W M ) 2 ) {\textstyle ((\mathrm {WM} )^{2})} as a satellite event of ICM. The International Commission on the History of Mathematics (ICHM) is operated jointly by the IMU and the Division of the History of Science (DHS) of the International Union of History and Philosophy of Science (IUHPS). The Committee on Electronic Information and Communication (CEIC) advises IMU on matters concerning mathematical information, communication, and publishing. The scientific prizes awarded by

4399-547: The age of 10, and his mother enrolled him in Sergei Rukshin's after-school mathematics training program. His mathematical education continued at the Leningrad Secondary School 239 , a specialized school with advanced mathematics and physics programs. Perelman excelled in all subjects except physical education . In 1982, not long after his sixteenth birthday, he won a gold medal as a member of

4482-449: The assumptions of the Poincaré conjecture , the Ricci flow with surgery exists only for finite time, so that the infinite-time analysis of Ricci flow is irrelevant. The construction of Ricci flow with surgery has the Poincaré conjecture as a corollary. In order to settle the Thurston conjecture , the second half of Perelman's second preprint is devoted to an analysis of Ricci flows with surgery, which may exist for infinite time. Perelman

4565-465: The attention of the mathematical community, although they were widely seen as hard to understand since they had been written somewhat tersely. Against the usual style in academic mathematical publications, many technical details had been omitted. It was soon apparent that Perelman had made major contributions to the foundations of Ricci flow , although it was not immediately clear to the mathematical community that these contributions were sufficient to prove

4648-457: The award, stating: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo." On 22 December 2006, the scientific journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific " Breakthrough of the Year ", the first such recognition in the area of mathematics. On 18 March 2010, it was announced that he had met the criteria to receive

4731-673: The conjecture. He had previously rejected the prestigious prize of the European Mathematical Society in 1996. Grigori Yakovlevich Perelman was born in Leningrad , Soviet Union (now Saint Petersburg, Russia) on June 13, 1966, to Jewish parents, Yakov (who now lives in Israel) and Lyubov (who still lives in Saint Petersburg with Perelman). Perelman's mother Lyubov gave up graduate work in mathematics to raise him. Perelman's mathematical talent became apparent at

4814-467: The extension of a well-known theorem of Nikolai Efimov to higher dimensions. Perelman's first works to have a major impact on the mathematical literature were in the field of Alexandrov spaces , the concept of which dates back to the 1950s. In a very well-known paper coauthored with Yuri Burago and Mikhael Gromov , Perelman established the modern foundations of this field, with the notion of Gromov–Hausdorff convergence as an organizing principle. In

4897-474: The field of mathematics. The article implies that Perelman refers particularly to alleged efforts of Fields medalist Shing-Tung Yau to downplay Perelman's role in the proof and play up the work of Cao and Zhu . Perelman added: "I can't say I'm outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest...It

4980-482: The first Clay Millennium Prize for resolution of the Poincaré conjecture. On 1 July 2010, he rejected the prize of one million dollars, saying that he considered the decision of the board of the Clay Institute to be unfair, in that his contribution to solving the Poincaré conjecture was no greater than that of Richard S. Hamilton , the mathematician who pioneered the Ricci flow partly with the aim of attacking

5063-472: The former of which had been a famous open problem in mathematics for the past century. The full details of Perelman's work were filled in and explained by various authors over the following several years. In August 2006, Perelman was offered the Fields Medal for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow", but he declined

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5146-436: The introduction of certain monotonic quantities and a "pseudolocality theorem" which relates curvature control and isoperimetry . However, despite being major results in the theory of Ricci flow, these results were not used in the rest of his work. The first half of Perelman's second preprint, in addition to fixing some incorrect statements and arguments from the first paper, used his canonical neighborhoods theorem to construct

5229-442: The medal later; third, I don't accept the prize. From the very beginning, I told him I have chosen the third one ... [the prize] was completely irrelevant for me. Everybody understood that if the proof is correct, then no other recognition is needed. " He was quoted as saying: " I'm not interested in money or fame, I don't want to be on display like an animal in a zoo. I'm not a hero of mathematics. I'm not even that successful; that

5312-512: The medal, which made him the only person to have ever declined the prize. He has also rejected a prestigious prize from the European Mathematical Society . On 18 March 2010, Perelman was awarded a Millennium Prize for solving the problem. On 8 June 2010, he did not attend a ceremony in his honor at the Institut Océanographique de Paris to accept his $ 1 million prize. According to Interfax , Perelman refused to accept

5395-442: The members of the executive committee. All important decisions are made at the GA, including the election of the officers, establishment of commissions, the approval of the budget, and any changes to the statutes and by-laws. The IMU has 83 (full) Member countries and two Associate Members ( Bangladesh and Paraguay , marked below by light grey background). The IMU has five affiliate members: The International Mathematical Union

5478-553: The methods introduced by Perelman. " " In this paper, we shall present the Hamilton-Perelman theory of Ricci flow. Based on it, we shall give the first written account of a complete proof of the Poincaré conjecture and the geometrization conjecture of Thurston. While the complete work is an accumulated efforts of many geometric analysts, the major contributors are unquestionably Hamilton and Perelman. [...] In this paper, we shall give complete and detailed proofs [...] especially of Perelman's work in his second paper in which many key ideas of

5561-490: The plane which is complete can be continuously immersed as a polyhedral surface. Later, he constructed an example of a smooth hypersurface of four-dimensional Euclidean space which is complete and has Gaussian curvature negative and bounded away from zero. Previous examples of such surfaces were known, but Perelman's was the first to exhibit the saddle property on nonexistence of locally strictly supporting hyperplanes. As such, his construction provided further obstruction to

5644-553: The promotion of mathematics in developing countries in the early 1970s and has, since then supported various activities. In 2010 IMU formed the Commission for Developing Countries (CDC) which brings together all of the past and current initiatives in support of mathematics and mathematicians in the developing world. Some IMU Supported Initiatives: IMU also supports the International Commission on Mathematical Instruction (ICMI) with its programmes, exhibits and workshops in emerging countries, especially in Asia and Africa. IMU released

5727-427: The proofs are sketched or outlined but complete details of the proofs are often missing. As we pointed out before, we have to substitute several key arguments of Perelman by new approaches based on our study, because we were unable to comprehend these original arguments of Perelman which are essential to the completion of the geometrization program. " In May 2006, a committee of nine mathematicians voted to award Perelman

5810-613: The report: The International Mathematical Union in the Developing World: Past, Present and Future (July 2014). In 2014, the IMU held a day-long symposium prior to the opening of the International Congress of Mathematicians (ICM), entitled Mathematics in Emerging Nations: Achievements and Opportunities (MENAO). Approximately 260 participants from around the world, including representatives of embassies, scientific institutions, private business and foundations attended this session. Attendees heard inspiring stories of individual mathematicians and specific developing nations. List of presidents of

5893-410: The set of regular points has the structure of a manifold modeled on DC functions. For his work on Alexandrov spaces, Perelman was recognized with an invited lecture at the 1994 International Congress of Mathematicians . In 1972, Jeff Cheeger and Detlef Gromoll established their important soul theorem . It asserts that every complete Riemannian metric of nonnegative sectional curvature has

5976-485: The setting of Ricci flow. By carrying out the proof of the Bishop–Gromov inequality for the resulting Li−Yau length functional, Perelman established his celebrated "noncollapsing theorem" for Ricci flow, asserting that local control of the size of the curvature implies control of volumes. The significance of the noncollapsing theorem is that volume control is one of the preconditions of Hamilton's compactness theorem . As

6059-553: The societies which are themselves members of the EMS, along with delegates representing the institutional and individual EMS members. The Council meets every 2 years, and appoints the President and Executive Committee who are responsible for the running of the society. Besides the Executive Committee, the EMS has standing committees on: Applications and Interdisciplinary Relations, Developing Countries, Mathematical Education, ERCOM (Directors of European Research Centres in

6142-471: The tentative title The Formula of the Universe . Zabrovsky says that in the interview, Perelman explained why he rejected the one million dollar prize. A number of journalists believe that Zabrovsky's interview is most likely a fake, pointing to contradictions in statements supposedly made by Perelman. The writer Brett Forrest briefly interacted with Perelman in 2012. A reporter who had called him

6225-419: The three-dimensional case, as their topological manipulations, moving "problematic regions" out of the way without interfering with other regions, seem to require high dimensions in order to work. In 1982, William Thurston developed a novel viewpoint, making the Poincaré conjecture into a small special case of a hypothetical systematic structure theory of topology in three dimensions. His proposal, known as

6308-497: The world is invited to join IMU as an Associate Member. For the purpose of facilitating jointly sponsored activities and jointly pursuing the objectives of the IMU, multinational mathematical societies and professional societies can join IMU as an Affiliate Member. Every four years, the IMU membership gathers in a General Assembly (GA), which consists of delegates appointed by the Adhering Organizations, together with

6391-444: The worldwide mathematical community by reporting on decisions and recommendations of the Union, major international mathematical events and developments, and on other topics of general mathematical interest. IMU Bulletins are published annually with the aim to inform IMU's members about the Union's current activities. In 2009 IMU published the document Best Current Practices for Journals . The IMU took its first organized steps towards

6474-414: The year he began graduate studies, he published an article controlling the size of circumscribed cylinders by that of inscribed spheres . Surfaces of negative curvature were the subject of Perelman's graduate studies. His first result was on the possibility of prescribing the structure of negatively-curved polyhedral surfaces in three-dimensional Euclidean space . He proved that any such metric on

6557-773: Was established in 1920, but dissolved in September 1932 and reestablished in 1950 at the Constitutive Convention in New York, de jure on September 10, 1951, when ten countries had become members. The last milestone was the General Assembly in March 1952, in Rome, Italy where the activities of the new IMU were inaugurated and the first Executive Committee, President and various commissions were elected. In 1952

6640-650: Was invited to spend a semester each at the Courant Institute in New York University , where he began work on manifolds with lower bounds on Ricci curvature . From there, he accepted a two-year Miller Research Fellowship at the University of California, Berkeley , in 1993. After proving the soul conjecture in 1994, he was offered jobs at several top universities in the US, including Princeton and Stanford , but he rejected them all and returned to

6723-472: Was only with Thurston's systematic viewpoint that most topologists came to believe that the Poincaré conjecture would be true. At the same time that Thurston published his conjecture, Richard Hamilton introduced his theory of the Ricci flow . Hamilton's Ricci flow is a prescription, defined by a partial differential equation formally analogous to the heat equation , for how to deform a Riemannian metric on

6806-469: Was unable to resolve Hamilton's 1999 conjecture on long-time behavior, which would make Thurston's conjecture another corollary of the existence of Ricci flow with surgery. Nonetheless, Perelman was able to adapt Hamilton's arguments to the precise conditions of his new Ricci flow with surgery. The end of Hamilton's argument made use of Jeff Cheeger and Mikhael Gromov 's theorem characterizing collapsing manifolds . In Perelman's adaptation, he required use of

6889-569: Was working on other things, but that it was too premature to discuss them. Perelman has shown interest in the Navier–Stokes equations and the problem of their solutions' existence and smoothness , according to Le Point . In 2014, Russian media reported that Perelman was working in the field of nanotechnology in Sweden . Shortly thereafter, however, he was spotted again in his native hometown of Saint Petersburg . Russian media speculated he

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