Master's Thesis
45 pages
I completed my Master's thesis under the supervision of Professor Paolo Cascini at Imperial on the Minimal Model Program. This program for higher-dimensional varieties was kickstarted by the Fields medalist Shigefumi Mori with his two key theorems: the cone theorem and the contraction theorem. I concentrate in my thesis on the cone theorem, motivated mainly by the beautiful techniques Mori utilised to arrive at this remarkable theorem.
Keywords: Birational Geometry, Deformation Theory
UROP Project
59 pages
Sheaves are a foundational construction in modern algebraic geometry. This article is a soft introduction to sheaf theory, without any reference to schemes. In fact, the only pre-requisite for the article is some prior experience with varieties. The aim of the article is to develop cohomology theory for sheaves and apply it in the classification of algebraic curves. I wrote this article as a part of the Undergraduate Research Opportunities Programme, which was supervised by Professor Johannes Nicaise.
Keywords: Algebraic Curves, Riemann-Roch
Expository Article
3 pages
As I learnt more and more geometry during my undergraduate degree and pondered its relation to other fields of mathematics, I came to the conclusion that gluing constructions are one of the most profound characteristics of geometry as a subfield. This article is aimed at general audience and it attempts to provide a feel for what gluing means in geometry. This article was my submission to the Oxford Invariants writing contest held in 2024. Even though it didn't get accepted, I hope you will find it interesting.
Keywords: Topology, Geometry
PhD Thesis
Keywords: Algebraic Geometry
