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Vladimir Touraev





© H. Raguet/CNRS Photothèque


The blackboard is wiped clean, the papers sorted, the pencils put away. In a few days, CNRS senior researcher Vladimir Touraev will be in Denmark with his family. And as usual, his primary port of call will be... a mathematics laboratory. “Research scientists are like the people who used to work in guilds: They learn their trade by traveling,” he says. “It is vital to go and meet your colleagues, especially these days when it is impossible to read all the scientific publications.” For Touraev, this is more than just a philosophy–it is a way of life. He receives invitations from all over the planet and spends three months abroad each year. His passion is topology, a branch of geometry that ignores distances. “In that universe, two circles of different sizes are equivalent objects,” explains Touraev. “We don't pay attention to object metrics: The only thing that matters is that you can make one object look like another by deforming it.” A strange world, where a square is equivalent to a circle... Our enthusiastic research scientist launches into a short but crystal-clear presentation on topology: The blackboard is soon covered with strange-looking braids, knots, and other intertwining objects.

Since he started his career, Touraev has worked on the links between his field (pioneered by Henri Poincaré) and physics. In 1989, he helped create the Topological Quantum Field Theory, which provides rigorously-defined mathematical objects to quantum mechanics. “Applications of this theory mainly concern theoretical physics, because there are few objects in the real world that are independent of their metrics,” notes the CNRS 2004 Silver Medal award winner. But if you push him a little, he will admit that his theory could help researchers create a quantum computer, no less. Yet he does not appear to be particularly thrilled: “First, we will have to come up with suitable algorithms,” he notes. “Otherwise, the computation speed may be the death knell for IT security and banking secrecy.”

But Touarev wasn't born in mathematics. In fact, as a child, he dreamed of becoming stage director, probably due to the fact that his father managed an important puppet theater in St. Petersburg (formerly Leningrad) and his mother was a theater critic. But by the age of 13, he had already developed his love of numbers, and entered a high school reserved for the scientific elite of the USSR. He attended the University of St. Petersburg and then the prestigious Steklov Institute of the Russian Academy of Sciences, where he continued his brilliant career, which attracted attention well beyond the Russian borders.

By the end of the 1980s, the Soviet Union had reached its final hour. Political uncertainty, a decaying economy, and the desire to see the world got the better of his ties to home. Touraev chose France because of its excellent reputation in mathematical research, and went to Strasbourg to join a friend who worked there as a research scientist. And what does this Russian citizen remember about his arrival in France? “I enjoyed the problems I faced, such as learning French,” he says, smiling. Fifteen years later, he speaks the language fluently. He continues to work on the alphabet, but for scientific purposes only: With topology tools, the series of letters “aabab” can be transformed (just like a square can be transformed into a circle) into “babaa,” and “ababa” can be shortened to “aa.” The topology of words, as he calls it, could open doors to the cryptology of tomorrow.


Matthieu Ravaud 

Contacts :

Vladimir Touraev
Institut de recherche mathématique avancée, Strasbourg.


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