Lecture Series by M. Kontsevich 2004

Some Information:

Maxim Kontsevich
Fields Medal 1998,
French Academy of Sciences 2002.
Legeon d'Heneur 2004.

Maxim Kontsevich has established a reputation in pure mathematics and theoretical physics, with influential ideas and deep insights. He has been influenced by the work of Richard Feynmann and Edward Witten. Kontsevich is an expert in the so-called "string theory" and in quantum field theory. He made his name with contributions to four problems of geometry. He was able to prove a conjecture of Witten and demonstrate the mathematical equivalence of two models of so-called quantum gravitation. The quantum theory of gravity is an intermediate step towards a complete unified theory. It harmonizes physical theories of the macrocosm (mass attraction) and the microcosm (forces between elementary particles). Another result of Kontsevich relates to knot theory. Knots mean exactly the same thing for mathematicians as for everyone else, except that the two ends of the rope are always jointed together. A key question in knot theory is, which of the various knots are equivalent? Or in other words, which knots can be twisted and turned to produce another knot without the use of scissors? This question was raised at the beginning of the 20th century, but it is still unanswered. It is not even clear which knots can be undone, that is, classifying all knots. They would be assigned a number or function, with equivalent knots having the same number. Knots which are not equivalent must have different numbers. However, such a characterization of knots has not yet been achieved. Kontsevich has found the best "knot invariant" so far. Although knot theory is part of pure mathematics, there seem to be scientific applications. Knot structures occur in cosmology, statistical mechanics and genetics.

Maxim Kontsevich (born 25 August 1964) is professor at the Institute des Hautes Etudes Scientific (I.H.E.S) in France.