Igor Krichever is the founding Director of the Center of Advanced Studies at Skolkovo Institute for Science and Technology, Moscow, a Professor of Mathematics at Columbia University, New York, and he is an Academic advisor of the program «Mathematics and Mathematical Physics» at Moscow Research University «Higher School of Economic». His main interests are in the theory of integrable systems and their application. In particular, he is known for developing an algebraic-geometric integration scheme of nonlinear soliton equations based on the concept of the Baker — Akhiezer function, and for the proof of the Trisecant conjecture, which provides a solution to the classical Riemann-Schottky problem on the characterization of Jacobians among principally polarized Abelian varieties. His other results include the Witham perturbation theory of integrable equations, the algebraic-geometrical spectral theory of two-dimensional periodic differential operators, a construction of Laurent-Fourie-type basis on algebraic curves and related generalization of Kac-Moody algebras. Jointly with S.Grushevsky he solved the classical, known since 19th century, problem on characterization of Prym varieties by proving that they are characterized by the existence of a pair of symmetric quadrisecants.
For his achievements he was awarded the Prize of Moscow Mathematical Society, he gave an invited talk at the ICM in 1990 and a plenary talk at the International Congress of Mathematical Physics (Lisbon, 2003).