From October 2009 to April 2013, I worked on a Ph.D in Mathematical Logic at the University of Leeds.
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.