Seminars

1pm Tuesday 10 March 2009, Lecture theatre S4 - Building 25, Clayton Campus
School of Mathematical Sciences Public Lecture
The structure of three dimensional curved space
Professor Klaus Ecker (Free University Berlin and Monash)

This lecture is a pictorial journey through two dimensional and three dimensional curved space. In two dimensions, there are only spherical geometry (positive curvature), hyperbolic geometry (negative curvature) and Euclidean (or flat) geometry (zero curvature).

In three dimensions, there are eight possible geometric structures. This is a lot harder to visualize, as many three dimensional spaces lie inside four (or higher) dimensional ambient spaces.

Through the joint efforts of many scientists over the last two thousand years, but particularly through the work of the mathematicians Poincare, Thurston, Hamilton and Perelman, a complete geometric and topological classification of all closed three dimensional spaces has now been achieved. In 2006, the Russian mathematician Grigori Perelman was awarded the Fields Medal for his groundbreaking contribution to the solution of this age old problem.