The Poincare Conjecture and Algorithmic Problems in Algebra
 
 
Description:  It has been announced that the Poincare Conjecture (claiming that any simply connected closed compact three-dimensional manifold is homeomorphic to the sphere), one of the most famous problems in mathematics, has been solved by Grisha Perelman of St.Petersburg. Although no complete verifiable proof has yet been written down, most experts believe that Perelman's argument is basically sound. The talk, however, will not focus on this proof (too complicated to be sketched in a one hour talk), but rather on an unexpected relationship between the undecidability of certain algorithmic problems of group theory and the Poincare Conjecture, as well as some computational aspects of the theory of 3-manifolds.

Alexey Sossinsky is a Professor at and Vice-President of the Independent University of Moscow (IUM) and, until recently, the Director of the French-Russian Poncelet Mathematics Laboratory (CNRS-IUM). He has held positions at Moscow State University (MSU), the Moscow Institute of Electronics and Mathematics (MIEM), the Institute for Problems in Mechanics of the Russian Academy of Sciences and visiting positions at the universities of Bordeaux, Rennes and Caen. Born in Paris of Russian parents, he was educated in France, in the United States, and in the Soviet Union. He obtained his BS degree from New York University in 1957, where he studied logic and topology under Jean van Heijenoort, his Master's (1961) and PhD (1965) degrees at MSU, where he wrote his PhD thesis on "Multidimensional Topological Knots" under the direction of L.V.Keldysh. In 1974, he was forced to resign his position at P.S.Alexandrov's Topology Chair at MSU for political reasons, and then worked as the Mathematics Editor of the popular science magazine "Kvant" under A.N.Kolmogorov until 1989, when he returned to teaching and research (at MIEM). He was one of the founders of the IUM, where now does most of his reaching. A.Sossinsky is the author or coauther of four books, about 60 research articles in geometric and algebraic topology, in mathematical linguistics, as well as numerous popular science booklets. His book on the history of knot theory ("Knots: Mathematics with a Twist") has been published in six languages. He is on the editorial board of five mathematical journals and the translator and/or editor of numerous books, including the AMS book series "Advances in Soviet Mathematics". His research interests include geometric and algebraic topology (with applications to finite difference methods), low-dimensional topology (in particular knot theory and Vassiliev invariants), algorithm and complexity theory (especially undecidable problems in algebra), mathematical linguistics (including computer translation), mathematical education and the popularization of mathematics.
Area(s):
Start Date:  2005-09-12
Start Time:   11:00
Speaker:  Alexey Sossinsky (Indep. Univ. Moscow)
Place:  Sala 2.4 - Departamento de Matemática
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