# Peter Nelson

E-mail: apnelson@uwaterloo.ca

Office: MC5128

Department of Combinatorics and Optimization

University of Waterloo

Waterloo, ON N2L3G1

Canada

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 theory. My **PhD thesis** deals with extremal problems relating to excluding a uniform matroid as a minor.

I recently 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 my papers - some are preprints:

**The maximum-likelihood decoding threshold for graphic codes.**

*Submitted. With Stefan van Zwam.*

**On the probability that a random subgraph contains a circuit**

*Submitted.*

**The densest matroids in minor-closed classes with exponential growth rate**

*Submitted. With Jim Geelen*

**Linkages in a directed graph with parity restrictions**

*Submitted. With Rutger Campbell.*

**The critical number of dense triangle-free binary matroids**

*JCTb, to appear. With Jim Geelen*

**Odd circuits in dense binary matroids**

*Combinatorica, to appear. With Jim Geelen.*

**The number of lines in a matroid with no U_{2,n}-minor**

*European J. Combin., to appear. 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. *