Maybe in its simplest form, the intimate connection between geometry and algebra is reflected in the fact that a circle with radius 1 is nothing but the collection of coordinates (x,y) solving the equation x² + y² = 1.
In this course, we will achieve a theoretic understanding of
affine and projective varieties,
their description in terms of algebraic equations,
or in terms of rings and ideals,
their topological properties,
maps between varieties,
and abstract notions such as sheaves and schemes.
Practically, there will be lots of pictures and geometrical examples, as well as hands-on work with computer algebra tools. The course will be worth 9 credit points. It is designed for Bachelor and Master students of mathematics, who will be able to register via RWTHonline. The material will be essentially (a subset of) Andreas Gathmann's lecture notes:
The team consists of Johannes Flake, Tom Görtzen, Verity Mackscheidt, and Jan Rodriguez. Looking forward to seeing you in the spring!