Projective Geometry 101 | Nat Kendal-Freedman

AMATH Grad Students

Candidate

Nat Kendal-Freedman | University of Waterloo

Title

Projective Geometry 101

Abstract

Two-dimensional projective geometry studies properties of points and lines which are invariant under projections. Thus, the key transformations preserve collinearity, rather than distance and length.

We begin with basic concepts such as quadrangles and perspectivities. To demonstrate the relation between different geometries, we show that a projective plane can be viewed as the completion of an affine plane and discuss the real projective plane. Finally, we cover the principle of duality to demonstrate the amazing symmetry between points and lines in projective space.

This talk is designed for people with no prior knowledge of projective geometry - we will start from the axioms!