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.

** A Ramsey theorem for biased graphs**

*Submitted. With Sophia Park.*

** Bounding χ by a fraction of Δ for graphs without large cliques**

*Submitted. With Marthe Bonamy, Tom Kelly and Luke Postle.*

** Stability and exact Turan numbers for matroids**

*Submitted. With Hong Liu, Sammy Luo and Kazuhiro Nomoto.*

**The extremal function for geometry minors of matroids over prime fields**

*Submitted. With Zachary Walsh.*

**Matroids with no U_{2,n}-minor and many hyperplanes**

*Adv. Appl. Math., to appear. With Adam Brown.*

** Doubly exponentially many Ingleton matroids**

*SIAM J. Discrete Math., to appear. With Jorn van der Pol.*

**Almost all matroids are non-representable**

*Bull. London Math. Soc. 50 (2018), 245-248.*

**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. *