Perelman ([19], [20]) used Ricci flow and its surgery to prove

Poincare conjecture. The Ricci flow is an evolution equation for metrics on a Riemannian manifold defined as follows:

Fermat's Last Theorem, The

Poincare Conjecture, Isaac Newton and Einstein are just some of the fascinating stories and personalities the students have been able to explore with Jarad.

Clay Research Conference: Resolution of the

Poincare Conjecture (2010: Paris, France) Edited by James Garlson

More recently, Grigory Perelman, a Russian, won the Fields Medal for his proof of the famous topological problem known as the

Poincare Conjecture.

Sobolev inequalities, heat kernels under Ricci flow, and the

Poincare conjecture.

Perelman, 43, said he believes his contribution in proving the

Poincare conjecture was no greater than that of US mathematician Richard Hamilton, who first suggested a program for the solution.

The 44- year- old mathematician had solved the

Poincare conjecture, which deals with shapes that exist in four or more dimensions rather than the familiar three.

Certain aspects of Perelman's work on the

Poincare conjecture have applications in physics and we want to suggest a few formulas in this direction; a fuller exposition will appear in a book in preparation [8].

Petersburg solved the "

Poincare Conjecture." His solution won Perelman math's highest honor, the Fields Medal, described as the mathematical equivalent of the Super Bowl.

The Clay outfit offers $1 million for the solution to any of seven long-standing puzzles in mathematics, and the

Poincare conjecture is one of them.

The

Poincare Conjecture involves the study of shapes, spaces and surfaces and makes predictions about the topology of multi-dimensional objects.

Disguised spheres A Russian mathematician offered a proof of the

Poincare conjecture, a question about the shapes of three-dimensional spaces, but it remained unclear whether the proof is solid (163: 259, 378 *).