Honours Seminar

Algebraic objects are often abstract and intuitions have mostly came from experience. The Category of Affine Schemes over $K$, being anti-equivalent to the Category of $K-algebra$ provides us a way of looking at abstract algebraic objects - Algebras, as concrete Geometrical objects - Affine Schemes. Pushing the same idea a little bit further, we can similarly look into a more specific set of Geometrical objects - affine group schemes, which corresponds to the algebraic object - Hopf Algebra.
In this talk I'll first introduce the idea of an Affine scheme through the functorial point of view and show how continuing on this idea allows us to view a more specific type of Algebra - Hopf Algebras, as Geometrical objects too. To save time and since Sam had talked about Categories, I'll assume we all know what it is and skip defining it.