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Geometry-Topology Seminar

Thursday, March 1, 2007 - 4:45pm

Hermann Karcher

University of Bonn

Location

University of Pennsylvania

DRL 4C8

If we look at 2-dim images of 3-dim objects of unknown shape, then the reconstruction of the object, that our brain makes from the 2-dim picture may be a significant distortion. I will show red-green stereo images from which the brain reconstructs the 3-dim objects fairly correctly. The objects are from mathematics: space curves of constant curvature, normal holonomy of torus knots, constructions on the 2-sphere that are analogous to familiar constructions in the plane, orbits of charged particles in magnetic fields, images of elliptic functions on the Riemann sphere, embedded rhombic(!) tori, linked tori made of Hopf fibres and more if the time permits.