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Peter NelsonE-mail: apnelson@uwaterloo.ca Office: MC5128
Department of Combinatorics and Optimization
I am an Associate 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 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. Here are the slides for an talk on binary matroids I gave in May 2019 at CanaDAM. Here is my CV and here are download or arXiv links to my papers in their current state, in roughly reverse chronological order. 38. Typical structure of hereditary properties of binary matroids 37. Excluding a line from complex-representable matroids 36. The structure of I_4-free and triangle-free binary matroids 35. The smallest matroids with no large independent flat 34. The critical number of I_{1,t}-free binary matroids. 33. Enumeration of extensions of the cycle matroid of a complete graph 32. The smallest I_5-free and triangle-free binary matroids. 31. The structure of claw-free binary matroids 30. On the number of biased graphs 29. The structure of binary matroids with no induced claw or Fano plane restriction
28. A Ramsey theorem for biased graphs 27. Bounding χ by a fraction of Δ for graphs without large cliques 26. Stability and exact Turan numbers for matroids 25. The extremal function for excluding geometry minors over prime fields 24. Matroids with no U_{2,n}-minor and many hyperplanes 23. Doubly exponentially many Ingleton matroids 22. Almost all matroids are non-representable 21. The structure of matroids with a spanning clique or projective geometry 20. On the probability that a random subgraph contains a circuit 19. The densest matroids in minor-closed classes with exponential growth rate 18. The maximum-likelihood decoding threshold for graphic codes 17. Linkages in a directed graph with parity restrictions 16. The critical number of dense triangle-free binary matroids 15. The number of lines in a matroid with no U_{2,n}-minor 14. Odd circuits in dense binary matroids 13. Matroids denser than a clique 12. Matroids representable over fields with a common subfield 11. Matroids denser than a projective geometry 10. On the existence of asymptotically good linear codes in minor-closed classes 9. Projective geometries in exponentially dense matroids, II 8. Projective geometries in exponentially dense matroids, I 7. A density Hales-Jewett theorem for matroids 6. An analogue of the Erdős-Stone theorem for finite geometries 5. The number of rank-k flats in a matroid with no U_{2,n}-minor 4. Growth rate functions of dense classes of representable matroids 3. On minor-closed classes of matroids with exponential growth rate 2. The number of points in a matroid with no n-point line as a minor 1. Sequential automatic algebras 0. Exponentially dense matroids |