Peter Nelson completed his PhD in Matroid Theory, under the supervision of Jim Geelen, in 2011. His thesis entitled Exponentially Dense Matroids was quite exceptional, proving results that precisely control the extremal behaviour of minor-closed classes of matroids from surprisingly weak hypotheses. For example, he proved that, if M is a simple matroid with sufficiently large rank and M does not contain an n-point line as a minor, then |M|≤(qr(M)-1)/(q-1) where q is the largest prime-power ≤n-2. The proofs combine techniques from extremal combinatorics with geometric intuition and clever connectivity reductions. Five high quality papers have been extracted from Peter's thesis, two of which are single authored. One paper, solving a 15 year old conjecture, has already appeared in the Journal of Combinatorial Theory, Series B, which is widely regarded as the leading journal in combinatorics. At the spring 2012 convocation, Peter was awarded an Outstanding Achievement in Graduate Studies honour.
Since completing his doctorate, Peter Nelson has taken up a postdoctoral fellowship in Wellington, New Zealand, working under the supervision of Geoff Whittle, one of the world's leading matroid theorists. His research has taken a somewhat new direction, but the results have been just as impressive. He has proved a geometric extension of the Erdős-Stone Theorem and is working on extending Szemeredi's Regularity Lemma.