Notes

Masters Thesis

A Study in ‘A Study in Derived Algebraic Geometry’

Undergraduate at Imperial College London (2018-2022)

  • Galois Theory (First Iteration)

    A very long document I wrote with a friend in the summer of 1st year where we wrote all the algebra we knew at the time.

  • Galois Theory (Second Iteration)

    Less than 15 pages. I wrote this in 2nd year as an attempt to isolate the key part making the fundamental theorem of Galois theory work.

  • Category Theory (First Iteration)

    An info dump of all the category theory I knew in 2nd year winter.

  • Colloquium talk in 3rd year on Filters in Topology

  • Talk in 3rd year at the Warwick Imperial Conference (WIMP) on Schemes : the Manifolds of Algebraic Geometry

    Crystalisation of my understanding of the locally-ringed-space approach to schemes.

  • Colloquium talk in 3rd year on “Triangles, Yoneda and Homology”

  • Notes on Delta Sets

    During 3rd year algebraic topology class, highly dissatisfied with the messiness in Hatcher’s exposition of “delta complexes”, I decided to clean it up using delta sets which Hatcher does not use.

  • Covering Spaces (First Iteration)

    Also 3rd year, again dissatified with Hatcher’s exposition this time of covering spaces, I wrote this exposition in an attempt to clean up and hence isolate the key parts involved in the “fundamental theorem of covering spaces”.

  • Covering Spaces (Second Iteration)

    In this iteration, the “formalism” and the “algebraic topology” is further isolated. A key realisation : semi-locally simple connectedness is precisely “locally 1-categorically contractible” and this is an equivalent condition to being able to recover topological covering spaces from categorical ones (of the fundamental groupoid).

  • Presheaves

    Everything I knew about presheaves in 3rd year summer. Key part : phrasing everything in terms of the “total space” of a presheaf.