MOVIE + EXHIBITION by HERWIG HAUSER
(I spy with my little eye)
The children's game with this name consists in letting find the others a thing one child has chosen secretely among the objects around. Nothing but the color is disclosed. Good choices are things nobody is thinking of: The iris of the eye, a chestnut on a tree or the reflection of the sun in the nearby pond.
In algebraic geometry, just reveal a polynomial equation in three variables. Let others find its zeroset! How does it look like? They won't find it by browsing the surroundings --singular varieties are shy and tend to hide out. They may appear only virtually when we close our eyes.
The movie invites you to a journey where the actors and actresses are real algebraic surfaces. They have their own life, move, expand, retract, collapse, blow up or fade out. The geometric patterns may intrigue you because they seem so natural though you have never seen them before. Their simplicity stems from simple equations. Their novelty suggests that there is much more geometry to observe and study.
Thursday, 24: 19:00-19:30.
PULCHRA ES: Singularities of algebraic surfaces (Exhibition at the Congress site)
The exposition shows a number of visualizations of algebraic surfaces in real three space, most of them with singular points or curves. Such surfaces arise when solving real polynomial equations in three variables. The pictures were produced with the ray-tracing program POV-Ray, which allows both high quality and intuitive understanding.
Complementary texts explain the geometric and algebraic background of these varieties.
2004 © Copyright by Asociación International Congress of Mathematicians, ICM
2006 Madrid. All Rights Reserved.