Past Visitor

# Maxim Kontsevich

Affiliation

Mathematics

*From *Documenta Mathematica*:*

Maxim Kontsevich is known principally for his work on four major problems in geometry. In each case, it is fair to say that Kontsevich's work and his view of the issues has been tremendously influential to subsequent developments. These four problems are:

•Kontsevich presented a proof of a conjecture of Witten to the effect that a certain, natural formal power series whose coefficients are intersection numbers of moduli spaces of complex curves satisfies the Korteweg-de Vries hierarchy of ordinary, differential equations.

•Kontsevich gave a construction for the universal Vassiliev invariant for knots in 3-space, and generalized this construction to give a definition of pertubative Chern-Simons invariants for three dimensional manifolds. In so doing, he introduced the notion of Graph Cohomology which succinctly summarizes the algebraic side of the invariants. His constructions also vastly simplified the analytic aspects of the definitions.

•Kontsevich used the notion of stable maps of complex curves with marked points to compute the number of rational, algebraic curves of a given degree in various complex projective varieties. Moreover, Kontsevich's techniques here have greatly affected this branch of algebraic geometry. Kontsevich's formulation with Manin of the related Mirror Conjecture about Calabi-Yau 3-folds has also proved to be highly influential.

•Kontsevich proved that every Poisson structure can be formally quantized by exhibiting an explicit formula for the quantization.

Taubes, Clifford Henry. "The Work of Maxim Kontsevich," (1998)

Fields Medalist, 1998

Dates at IAS

*Visitor*

- Mathematics

*Member*

- Natural Sciences, Mathematics

Degrees

Bonn University

*Ph.D.,**1992*Honors

Fields Medal 1998

Prize of the International Congress of Mathematical Physics 1997

Prize of the Maire of Paris, 1st European Congress of Mathematics 1992

Appointments

Rutgers University, The State University of New Jersey
1997–

*Visiting Professor*
Institut des Hautes Études Scientifiques
1995–

*Professor of Mathematics*