Peter Nelson


Office: MC5128

Department of Combinatorics and Optimization
University of Waterloo
Waterloo, ON N2L3G1

I am an Assistant Professor in the Department of Combinatorics and Optimization at the University of Waterloo in Ontario, Canada.

My research interests are in structural and extremal matroid theory and graph theory, and more recently on their links with both coding theory and additive combinatorics. My PhD thesis deals with extremal problems relating to excluding a uniform matroid as a minor.

I organised the program for a small workshop in structural matroid theory held from July 6-10, 2015 in La Vacquerie, France. Recordings of the talks and slides can be found here.

Here is my CV and here are download or arXiv links to my papers in their current state:

Stability and exact Turan numbers for matroids
Submitted. With Hong Liu, Sammy Luo and Kazuhiro Nomoto.

Doubly exponentially many Ingleton matroids
Submitted. With Jorn van der Pol.

Matroids with no U_{2,n}-minor and many hyperplanes
Submitted. With Adam Brown.

Almost all matroids are non-representable

The extremal function for geometry minors of matroids over prime fields
Submitted. With Zachary Walsh.

The structure of matroids with a spanning clique or projective geometry
JCTb 127 (2017), 65-81. With Jim Geelen.

On the probability that a random subgraph contains a circuit
J. Graph Theory 85 (2017), 644-650.

The densest matroids in minor-closed classes with exponential growth rate
Trans. Amer. Math. Soc 369 (2017), 6751-6776. With Jim Geelen.

The maximum-likelihood decoding threshold for graphic codes
IEEE Trans. Inf. Theory 62 (2016), 5316-5322. With Stefan van Zwam.

Linkages in a directed graph with parity restrictions
Not submitted. With Rutger Campbell.

The critical number of dense triangle-free binary matroids
JCTb 116 (2016), 238-249. With Jim Geelen.

The number of lines in a matroid with no U_{2,n}-minor
European J. Combin. 50 (2016), 115-122. With Jim Geelen.

Odd circuits in dense binary matroids
Combinatorica 35 (2015), 730-735. With Jim Geelen.

Matroids denser than a clique
JCTb 114 (2015), 51-69. With Jim Geelen

Matroids representable over fields with a common subfield
SIAM J. Discrete Math. 29 (2015), 796-810. With Stefan van Zwam.

Matroids denser than a projective geometry
SIAM J. Discrete Math 29 (2015), 730-735.

On the existence of asymptotically good linear codes in minor-closed classes
IEEE Trans. Inf. Theory 61 (2015), 1153-1158. With Stefan van Zwam.

Projective geometries in exponentially dense matroids, II
JCTb 113 (2015), 185-207.

Projective geometries in exponentially dense matroids, I
JCTb 113 (2015), 208-219. With Jim Geelen.

A density Hales-Jewett theorem for matroids
JCTb 112 (2015), 70-77. With Jim Geelen.

An analogue of the Erdős-Stone theorem for finite geometries
Combinatorica 35 (2015), 209-214. With Jim Geelen.

The number of rank-k flats in a matroid with no U_{2,n}-minor
JCTb 107 (2014), 140-147.

Growth rate functions of dense classes of representable matroids
JCTb 103 (2013), 75-92.

On minor-closed classes of matroids with exponential growth rate
Adv. Appl. Math. 50 (2013), 142-154. With Jim Geelen.

The number of points in a matroid with no n-point line as a minor
JCTb 100 (2010), 625-630. With Jim Geelen.

Sequential automatic algebras
CiE (2008), 84-93. With Michael Brough and Bakhadayr Khoussainov.