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Friday, August 18, 2006

Grisha: cutting the singularities,to solve Poincare conjecture


The world mathematical elite is worried because next week (22 -30 of August), met the International Community of Mathematicians (ICM), will decide in base to careful studies to offer the Field Medal (Nobel Prize of Math), to the best mathematical contribution, of the last 4 years. By the same motives, this year, the Clay Mathematicians Institute, also will offer the Millennium Prize Problems (1 million dollars, to whom solve one of 7 math problems: Poincare conjecture, Yang-Mills Theory, P vs NP, Hodges conjecture, Hipothesis of Riemann, etc). The matter is that the world mathematical community, perceives that the prize must be offered to Gregory Y. (Grisha), Perelman (40), an exceptional Russian mathematician, little given to societary or monetary formalities, that has dedicated all his life to the study of the geometry of Riemmann and aspects related to topology. Grisha has declined does little the prize that the European Mathematic Society offered him. His most math contribution is the method employed for the solution of the conjecture of geometrization of Thurston (that includes the conjecture of Poincare). A different method that speaks of the brilliance of the human being and that will contribute to explain the form of the visible universe, how to travel through space wormholes and to explain a priori the distortions exercised by the gravity of large bodies (black holes) and the forms of the clouds of electrons that rotate around neutrons or protons, with plenty of property. Grisha, has not presented their solution of the conjecture of Poincaré to a mathematical magazine of elite for peer review, as require the prizes givers companies. Alone he has presented his works to the online edition of Arxiv (2002-2003.Cornell University). Besides it, since 2003 to the date, he has almost disappeared. It is said even that he has renounced to the famous Steklov Mathematics Institut, part of the Russian Academy of Sciences/St Peterburg, where he labored until does little.

In 1904 the last great general practitioners in math: Henry Poincare, presented his famous conjecture…"there is certain sufficient condition to assure that a geometric structure of various spaces, flat, dimensions or connections (manifold) -without holes- be homeomorphic to a sphere" …… If it had holes it will become in a doughnut, but not in a sphere. Although some mathematicians : (Stephen Smale: 1960, found the solution for manifolds of 5 or more dimensions) and Michael Freedman (1983), for 4 dimensions, the problem has remained elusive for 3 dimensions (3D), because the finite or infinite curvatures (singularities), of geometric bodies of 3D, stopped until does little its geometric mathematics. The last mathematician in presenting a solution for structures of 3D, has been the American Richard Hamilton, by means of application of differential equations to singularities (large curvatures or, geometric distortions), by-products of equations established for the heat, where the irregularities (hotspots, singularities), were treated by the equations step by step, until the irregularities go being dissipated (being smoothed), being reached a final, regular uniformity in geometric objects of finite volume. The method employed by Grisha Perelman -although sinks roots in the system of Hamilton- differs of it, because each time that he found singularities, instead of smoothing them, removes them (flow of Ricci, with surgery), handling them in form separated, but uniting them at the final, in general equations. Of that, always it comes find the soothing roads of the final sphere. With this method, the geometric curvatures always light up uniforms. The elite of present mathematicians, think that the flow of Ricci, can be applied to aspects or pieces done not work of the conjecture of Poincare, so that already they consider it resolved. Some mathematicians of renown: B. Kleiner (Yale), Morgan (Columbia), Gang Tian (Princeton), Huai Dong (Lehig University), have prepared several books of but of 500 pages to this respect.

Perelman :cortar singularidades para resolver conjetura de Poincaré.

La élite matemática mundial está preocupada porque la próxima semana (22 -30 de agosto), reunida la International Community of Mathematicians (ICM), decidirá en base a cuidadosos estudios otorgar el Field Medal (Premio Nobel de Matemáticas), a la mejor contribución matemática, de los últimos 4 años. Por los mismos motivos, este año, el Clay Mathematics Institute, tambien otorgará el Millennium Prize Problems (1 millón de dolares, a quien solucione uno de 7 problemas matemáticos : Poincaré conjecture, Yang-Mills Theory, P vs NP, Hodges conjecture, Hipothesis of Riemann, etc). El asunto es que la comunidad matemática mundial, percibe que el premio deberia ser otorgado a Gregory Y. (Grisha), Perelman (40), un excepcional matemático ruso, poco dado a formalidades societarias o monetarias, que ha dedicado toda su vida al estudio de la geometría de Riemmann y aspectos relacionados con la topologia. Grisha declinó hace poco el premio que le otorgara la European Mathematic Society. Su contribución matemática mas importante es el método empleado para la solución de la conjetura de geometrizacion de Thurston (que incluye la conjetura de Poincaré). Un metodo diferente que habla de la brillantéz del ser humano y que contribuira a explicar la forma del universo visible, viajar a traves de agujeros de gusano y explicar a priori las distorsiones ejercidas por la gravedad de grandes cuerpos (agujeros negros) y las formas de las nubes de electrones que giran alrededor de neutrones o protones, con bastante propiedad. Grisha, no ha presentado su solución de la conjetura de Poincaré a una revista matemática de elite para su revisión por pares, como exigen las entidades dadoras de premios. Solo ha presentado sus trabajos a la edicion online de Arxiv (2002-2003). Además desde el 2003 a la fecha, ha casi desaparecido. Se dice incluso que ha renunciado al famoso instituto Steklov Mathematics Institut, part of the Russian Academy of Sciences/St Peterburg, donde laboraba hasta hace poco.

En 1904 el último de los grandes generalistas en matemáticas : Henry Poincare, planteó su famosa conjetura…”hay cierta condición suficiente para asegurar que una estructura geométrica de varios espacios, planos, dimensiones o conexiones (manifold) -sin agujeros- sea homeomórfico a una esfera”…… Si tuviese agujeros (tasa, con asas), devendria en un doughnut, mas nó en una esfera. Aunque algunos matematicos (Stephen Smale :1960, encontró la solución para manifolds de 5 o más dimensiones) y Michael Freedman (1983), para 4 dimensiones, el problema ha permanecido elusivo para 3 dimensiones, por que las curvaturas finitas o infinitas (singularidades), de cuerpos geométricos de 3D, impedian hasta hace poco su matematizacion geometrica. El ultimo matemático en plantear una solución para estructuras de 3D, ha sido el americano Richard Hamilton, mediante la aplicación de ecuaciones diferenciales a singularidades (grandes curvaturas o, distorsiones geométricas), derivadas de ecuaciones establecidas para el calor, donde las irregularidades (hotspots, singularidades), son tratadas por las ecuaciones paso a paso, hasta que las irregularidades van disipandose (alisandose), alcanzandose al final una uniformidad regular en objetos geométricos de volumen finito. El método empleado por Grisha Perelman -aunque hunde raices en el sistema de Hamilton- difiere de el, porque cada vez que se encuentra con singularidades, en vez de alisarlas, las remueve (flujo de Ricci, con cirugía), manejandolas en forma separada, pero uniendolas al final a las ecuaciones generales. De ese, siempre se llega a encontrar los caminos conformantes de la esfera final. Con este metodo, las curvaturas geométricas siempre lucen uniformes. La elite de matemáticos actuales, piensan que el flujo de Ricci, puede ser aplicado a aspectos o piezas no trabajadas de la conjetura de Poincare, de modo que ya la consideran resuelta. Algunos matematicos de renombre : B. Kleiner (Yale), Morgan (Columbia), Gang Tian (Princeton), Huai Dong (Lehig University), han preparado varios libros de mas de 500 páginas al respecto.

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