Mathematics

Current

I’m moving to the University of Guildford.

 

Teaching

I was a lecturer of mathematics at Lincoln College, Oxford. Information onĀ  current and past teaching can be found here.

 

Interests

Here are some helpful resources, and pages and articles I like and find fascinating. There are also excellent books, but unless there is a link to the files I can find, I won’t put them here — perhaps on another page, on another day.

stochastic analysis, probability theory, ergodic theory, pdes:

analytic number theory

harmonic analysis

two special problems (special to me)

  • the Hadwiger conjecture states that if a graph is not k-colourable, then it has a complete-(k+1) minor; Robertson and Seymour havewritten lots about it, and here is a survey of results on the problem
  • the Erdos-Turan conjecture states that if an infinite collection (a_i) of increasing positive integers satisfies the density condition that the sum of their reciprocals is infinite, then that collection contains arbitrarily long arithmetic sequences. this is of course related to Szemeredi’s theorem, with a much weaker density condition. Green and Tao (Conlon, Fox, and Zhao’s exposition) pushed beyond Szemeredi’s positive Banach density condition to arithemtic progessions on the primes.

 

I’m currently reading Arora and Barak’s book on computational complexity and it is fascinating!