My research interests are in structural and extremal matroid theory and graph theory, and their links with coding theory, additive combinatorics and finite geometry, particularly the theory of minor-closed classes, and the binary matroids with the submatroid order and the induced submatroid order. I've also recently become interested in proof formalization in LEAN. I hold an NSERC Discovery Grant and an Early Researcher Award.

**38. Typical structure of hereditary properties of binary matroids **

*Submitted. With Stefan Grosser, Hamed Hatami and Sergey Norin.*

**37. Excluding a line from complex-representable matroids**

*Accepted, Memoirs Amer. Math. Soc. With Jim Geelen and Zachary Walsh.*

**36. The structure of I_4-free and triangle-free binary matroids**

*SIAM J. Discrete Math. 36 (2022), 1711-1729 , With Kazuhiro Nomoto.*

**35. The smallest matroids with no large independent flat **

*Electronic J. Combin. 28 (2021). With Sergey Norin.*

**34. The critical number of I_{1,t}-free binary matroids. **

*Submitted. With Kazuhiro Nomoto.*

**33. Enumeration of extensions of the cycle matroid of a complete graph**

*Adv. Appl. Math. 138, With Kazuhiro Nomoto.*

**32. The smallest I_5-free and triangle-free binary matroids.**

*Submitted. With Kazuhiro Nomoto.*

**31. The structure of claw-free binary matroids**

*JCTb 150 (2021), 76-118. With Kazuhiro Nomoto.*

**30. On the number of biased graphs**

*SIAM J. Discrete Math. 33, 373-382. With Jorn van der Pol.*

**29. The structure of binary matroids with no induced claw or Fano plane restriction
**

*Advances in Combinatorics. 1. With Marthe Bonamy, Frantisek Kardos, Tom Kelly and Luke Postle.*

**28. A Ramsey theorem for biased graphs**

*SIAM J. Discrete Math. 134 (2020), 2270-2281. With Sophia Park.*

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

*Accepted, JCTb. With Marthe Bonamy, Tom Kelly and Luke Postle.*

**26. Stability and exact Turan numbers for matroids**

*JCTb 143 (2020), 29-41. With Hong Liu, Sammy Luo and Kazuhiro Nomoto.*

**25. The extremal function for excluding geometry minors over prime fields**

*SIAM J. Discrete Math. 36 (2022), 2100-2120. With Zachary Walsh.*

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

*Adv. Appl. Math. 100 (2018), 143-147. With Adam Brown.*

**23. Doubly exponentially many Ingleton matroids**

*SIAM J. Discrete Math. 32, 1145-1153. With Jorn van der Pol.*

**22. Almost all matroids are non-representable**

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

**21. The structure of matroids with a spanning clique or projective geometry**

*JCTb 127 (2017), 65-81. With Jim Geelen.*

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

*J. Graph Theory 85 (2017), 644-650.*

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

*Trans. Amer. Math. Soc 369 (2017), 6751-6776. With Jim Geelen.*

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

*IEEE Trans. Inf. Theory 62 (2016), 5316-5322. With Stefan van Zwam.*

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

*Not submitted. With Rutger Campbell.*

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

*JCTb 116 (2016), 238-249. With Jim Geelen.*

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

*European J. Combin. 50 (2016), 115-122. With Jim Geelen.*

**14. Odd circuits in dense binary matroids**

*Combinatorica 35 (2015), 730-735. With Jim Geelen.*

**13. Matroids denser than a clique **

*JCTb 114 (2015), 51-69. With Jim Geelen*

**12. Matroids representable over fields with a common subfield**

*SIAM J. Discrete Math. 29 (2015), 796-810. With Stefan van Zwam.*

**11. Matroids denser than a projective geometry**

*SIAM J. Discrete Math 29 (2015), 730-735.*

**10. On the existence of asymptotically good linear codes in minor-closed classes **

*IEEE Trans. Inf. Theory 61 (2015), 1153-1158. With Stefan van Zwam.*

**9. Projective geometries in exponentially dense matroids, II**

*JCTb 113 (2015), 185-207.*

**8. Projective geometries in exponentially dense matroids, I**

*JCTb 113 (2015), 208-219. With Jim Geelen.*

**7. A density Hales-Jewett theorem for matroids**

*JCTb 112 (2015), 70-77. With Jim Geelen.*

**6. An analogue of the Erdős-Stone theorem for finite geometries**

*Combinatorica 35 (2015), 209-214. With Jim Geelen.*

**5. The number of rank-k flats in a matroid with no U_{2,n}-minor**

*JCTb 107 (2014), 140-147.*

**4. Growth rate functions of dense classes of representable matroids**

*JCTb 103 (2013), 75-92.*

**3. On minor-closed classes of matroids with exponential growth rate**

*Adv. Appl. Math. 50 (2013), 142-154. With Jim Geelen.*

**2. The number of points in a matroid with no n-point line as a minor**

*JCTb 100 (2010), 625-630. With Jim Geelen.*

**1. Sequential automatic algebras**

*CiE (2008), 84-93. With Michael Brough and Bakhadayr Khoussainov. *

**0. Exponentially dense matroids**

*Ph.D. Thesis, University of Waterloo*