Wolf Prize Laureate in Mathematics 2005
Sergei P. Novikov
Affiliation at the time of the award:
University of Maryland, USA
The L.D. Landau Institute for Theoretical Physics, Russia
“for his fundamental and pioneering contributions to algebraic and differential topology, and to mathematical physics, notably the introduction of algebraic-geometric methods”.
Professor Sergei P. Novikov is awarded the Wolf Prize for his fundamental and pioneering contributions to topology and to mathematical physics. His early work in algebraic and differential topology includes such milestones as the calculation of cobordism rings and stable homotopy groups, proof of the topological invariance of rational Pontrjagin Classes, formulation of the “Novikov Conjecture” on higher signature invariants, and proof of the existence of closed leaves in two-dimensional foliations of the 3-sphere.
In the early 1970s, Novikov turned his attention to mathematical physics, initially contributing to general relativity and conductivity of metals. He constructed a global version of Morse Theory on manifolds and loop spaces that had novel applications to quantum field theory (multi-valued action functionals). His most significant achievements in mathematical physics flow from his introduction of algebraic-geometric methods to the study of completely integrable systems. These include a systematic study of finite-gap solutions of two-dimensional integrable systems, formulation of the equivalence of the classification of algebraic-geometric solutions of the KP equation with the conformal classification of Riemann surfaces, and work (with Krichever) on “almost commuting” operators, that appear in string theory and matrix models (“Krichever-Novikov algebras”, now widely used in physics).
Novikov made a fundamental and striking contribution to two separate fields in mathematics, while he is one of those rare mathematicians who brings deep, key mathematical ideas to bear on difficult pivotal problems of physics, in ways that are stunning and compelling for both mathematicians and physicists.