I’m a fourth-year undergraduate at the University of Bristol. My primary interests are algebraic geometry, category theory and number theory. All things going well, I will be starting a PhD next year working on arithmetic geometry – particularly anabelian geometry, motives and the relations between topology and number theory. My hope is that in the future, armed with all this formidable technical machinery, I’ll be able to solve difficult but concrete problems in number theory.

That’s what this blog is about – it’s my “lab book” for the long process of solo-studying all this material, starting from the basics of scheme theory and building up to more tricky things. Writing on here will help my brain process and consolidate what I’ve been working on, and hopefully you might find it interesting to read and maybe even learn a few things too!

I got the name for this blog from a blog post by Jordan Ellenburg in which he discusses Mochizuki’s proof of the ABC Conjecture. He writes:

Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space.

This blog isn’t devoted to understanding Mochizuki’s construction – which he claims would take *ten years* for a seasoned geometer to learn – but I do hope to touch on some of the areas he works with and perhaps look at some of the new mathematical objects he builds in his proof. More generally I will broadly follow material from Liu’s *Algebraic Geometry and Arithmetic Curves *as well as other texts, and make interesting diversions along the way to many topics in arithmetic geometry.

Disclaimer: throughout this blog, I’m going to be writing a lot of proofs, and although I will have puzzled over a lot of them myself, some of them will undoubtedly be taken from books I’m reading! In keeping with the informal nature of this blog, I will rarely provide references when I do this, but I will maintain a “books” page listing resources I’ve used and found helpful.

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