Shapiro conjecture in real algebraic geometry and integrable systems
Shapiro conjecture says that if the Wronskian of a set of polynomials has
real roots only, then
the complex span of this set of polynomials has
a basis consisting of polynomials with real coefficients.
The proof of this fact is surprising. It is based on the theory of quantum integrable systems.
Professor Varchenko is a leading expert in Mathematical Physics, with way more than 200 publications and 1600 citations. His area of specialization lies in Topology, Algebraic Geometry and Singularity Theory.
He was a plenary speaker at the International Congress of Mathematicians in Kyoto, 1990. He was chosen a Clay Mathematics Institute Book Fellow for 2002. In 2008 he had been awarded the "Chaires d'Excellence Pierre de Fermat'', an award developed to attract top scientists in any discipline to spend time in France.