Title of the course: Affine and projective planes
Instructor: Prof. Adrien Deloro
Institution: Sorbonne Université
Dates: 25 July – 6 August 2022
Prerequisites: Abstract algebra: groups, rings, fields, finite-dimensional vector spaces; group actions.
Level: Advanced undergraduate
Abstract: You are all familiar with the usual affine plane over the reals, the one we use in elementary geometry. Perhaps you also know about the projective plane over the reals, ‘where lines meet at infinity’. But there is more. We can study affine/projective planes over any field (call them ‘concrete’). And we can even investigate `abstract’ affine/projective planes, pure geometries without a coordinate system, easily described axiomatically. To which extent concrete and abstract structures coincide provides illuminating relationships between combinatorial geometry and abstract algebra. This class will teach you think algebraically.
Language: EN