From October 2009 to April 2013, I worked on a Ph.D in Mathematical Logic at the University of Leeds.
My supervisors were the late S. Barry Cooper (obituary) and Andy Lewis.
Computability theory and algorithmic randomness
The topic of my thesis was computability theory, and more specifically algorithmic randomness.
I've written a quick introduction to algorithmic randomness for this website.
My full thesis is titled "Notions and applications of algorithmic randomness" (pdf, 801 kB).
Papers and other mathematical downloads:
- A new total injection betting strategy (September 2011) is my paper in which I give a direct construction of a partial computably random sequence which is not total injection random.
I presented an earlier version of the paper at the conference CiE 2011 in Sofia, Bulgaria.
- The Angel Problem was the subject of a couple of talks that I gave. Here are the slides:
- Problem 10 of the 2010 LIMO mathematics competition ask you to prove that certain matrices are nilpotent. The model solutions use the Cayley-Hamilton theorem. I give a purely combinatorial solution:
- Sequences and nets in topology is an expository article in which I show how sequences might fail to characterize topological properties such as openness, continuity and compactness correctly. Moreover, I define nets and show how they succeed where sequences fail.
- In Embeddings into the countable atomless Boolean algebra I prove that every countable distributive lattice embeds into the lattice of computable subsets of the natural numbers. This is a well known result, but a proof is nowhere to be found. I give a proof and explain some related mathematics.
- Realizability Toposes is the essay I wrote as part of Certificate of Advanced Study in Mathematics, commonly known as Part III, at the University of Cambridge in 2009.