A Public Lecture by Professor J. Hyam Rubinstein, Department of Mathematics & Statistics, University of Melbourne.
The Poincare conjecture was one of the most celebrated questions in mathematics. It was amongst the seven millennium problems of the Clay Institute, for which a prize of $1million was offered.
The Poincare conjecture asked whether a 3-dimensional space with `no holes’ is equivalent to the 3-dimensional sphere.
In 2003 Grigori Perelman posted three papers on the internet ArXiv outlining a marvellous solution to the Poincare conjecture, as part of the completion of Thurston’s geometrisation program for all 3-dimensional spaces. Perelman introduced powerful new techniques into Richard Hamilton’s Ricci flow, which `improves’ the shape of a space. Starting with any shape of a space with no holes, Perelman was able to flow the space until it became round and therefore verified it was a sphere.
A brief history of the Poincare conjecture and Thurston’s revolutionary ideas will be given. Hamilton’s Ricci flow will be illustrated.
Famously, Perelman turned down both the Clay prize and a Field’s medal for his work.
Cost: Free. RSVP to [email protected]