One of the hardest modules I took at Imperial was MATH70061 Commutative Algebra taught by Yankı Lekili. What made the module so challenging was the fact that we had to submit solutions to 6-8 tedious homework problems every 2 weeks. In addition, the course covered quite a broad selection of material, which we had to stay on top of. The …

Morphisms between affine varieties are determined simply by specifying a fixed number of polynomials. On the other hand, morphisms between projective varieties are not as easy to deal with in general and may sometimes require construction via _gluing_. If one tries to understand collections of morphism, it becomes tricky to keep track of all the "gluing data". This problem is …

I decided to start this blog by writing about my favourite proof that can be fit in a blog post and which put me on the track to learn algebraic geometry. I was originally fascinated by the connections that algebraic geometry makes between branches of mathematics and uses these to solve actual problems, which is what I saw nicely demonstrated …