Chercheurs

Mathématiques / PERELMAN, GRIGORI YAKOVLEVICH

Position

Russian mathematician
Former researcher at theSteklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia.

Thèmes de recherche

Thurston\'s geometrization conjecture, also known simply as the geometrization conjecture, states that compact 3-manifolds can be decomposed into pieces with geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces. It was proposed by William Thurston in the late 1970s, and implies several other conjectures, such as the Poincaré conjecture and Thurston\'s elliptization conjecture.

Grigori Perelman sketched a proof of the geometrization conjecture in 2003 using Ricci flow with surgery, which (as of 2006) appears to be essentially correct.

Prix et récompenses

2010 Millennium Prize of the Clay Mathematics Institute for resolution of the Poincaré conjecture.

Publications

G. Perelman, The entropy formula for the Ricci flow and its geometric applications, 2002

G. Perelman, Ricci flow with surgery on three-manifolds, 2003