1. Less Than Half of All Oriented Paths Are Anti-Sidorenko. Invited seminar talk, 2026. Combinatorics Seminar, University College London.
2. Less Than Half of All Oriented Paths Are Anti-Sidorenko. Invited conference talk, 2025. Winter Workshop in Combinatorics at LSE, London School of Economics & Political Science.
3. Maximizing the number of alternating walks in an edge-coloured graph. Contributed conference session talk, 2025. CanaDAM 2025, Minisymposium on Interdisciplinary Extremal Combinatorics, Ottawa.
4. Squaring the Circle with Simple Pieces. Invited colloquium talk, 2025. University of Chile, Department of Engineering Mathematics Colloquium, Santiago.
5. An Approximate Counting Version of the Multidimensional Szemerédi Theorem. Contributed conference talk, 2024. Discrete Math Days 2024, Alcalá de Henares, Spain.
6. Off-Diagonal Ramsey Multiplicity. Invited conference session talk, 2024. AMS Spring Western Sectional Meeting, Special Session on Extremal Combinatorics and Connections, San Francisco.
7. Some Trees are Always More Plentiful than Others. Invited seminar talk, 2023. Probability and Dynamics Seminar, University of Victoria.
8. Six Permutation Patterns Force Quasirandomness. Invited conference session talk, 2023. CanaDAM 2023, Minisymposium on Combinatorics and Algebra, Winnipeg.
9. Squaring the Circle with Simple Pieces. Invited colloquium talk, 2023. Masaryk University Mathematics Colloquium, Brno.
10. Minimizing copies of red copies of one graph and blue copies of another. Invited seminar talk, 2023. Atlantic Canada Graph Theory Seminar, online.
11. Solving HUGE Problems Quickly. Invited outreach talk, 2022. IMAGINING UVic, University of Victoria.
12. Common pairs of graphs. Invited conference talk, 2022. A Conference in Celebration of Bruce Reed’s Mathematical Career, University of Oxford.
13. Squaring the Circle with Graph Theory. Contributed seminar talk, 2022. Discrete Math Seminar, University of Victoria.
14. Forcing quasirandomness in permutations. Invited seminar talk, 2021. Algebraic Combinatorics Seminar, University of Waterloo.
15. Forcing quasirandomness in permutations. Invited seminar talk, 2021. SCMS Combinatorics Seminar, Shanghai.
16. Non-bipartite k-common graphs. Invited seminar talk, 2020. Extremal and Probabilistic Combinatorics Webinar, online.
17. Cycles of length three and four in tournaments. Invited seminar talk, 2020. Combinatorial Theory Seminar, University of Oxford.
18. Tarski's Circle Squaring Problem. Invited seminar talk, 2020. Math Club Seminar, Thompson Rivers University.
19. Forcing Quasirandomness in Permutations. Invited conference session talk, 2019. 32nd Brazilian Mathematics Colloquium, Thematic Session on Combinatorics, Rio de Janeiro.
20. Reconfiguring Graph Homomorphisms. Contributed conference talk, 2019. International Workshop on Combinatorial Reconfiguration (CoRe), Aussois.
21. Cycles of length three and four in tournaments. Invited conference session talk, 2019. CanaDAM 2019, Minisymposium on Analytic and Probabilistic Techniques in Combinatorics, Vancouver.
22. Cycles of length three and four in tournaments. Invited seminar talk, 2019. Joint DIMEA and FORMELA Seminar, Masaryk University, Brno.
23. Cycles of length three and four in tournaments. Invited seminar talk, 2019. Combinatorics Seminar, University of Birmingham.
24. Bootstrap percolation in high dimensions and related results. Invited seminar talk, 2019. Statistical Mechanics Seminar, University of Warwick.
25. Cycles of length three and four in tournaments. Invited seminar talk, 2019. Mathematical Sciences Seminar, Birkbeck University of London.
26. Supersaturation in Posets. Invited seminar talk, 2018. Discrete Mathematics and Optimization Seminar, McGill University.
27. Supersaturation in Posets. Invited seminar talk, 2018. Combinatorics Study Group Seminar, Queen Mary University of London.
28. Reconfiguring Graph Colourings and Homomorphisms. Invited conference session talk, 2018. SIAM Conference on Discrete Mathematics (SIAM DM18), Denver.
29. Reconfiguring Graph Colourings and Homomorphisms. Invited seminar talk, 2018. Combinatorics Seminar, University of Bristol.
30. How to Spread a Rumour in a High-Dimensional Network. Invited seminar talk, 2017. Mathematics Seminar, Thompson Rivers University.
31. Bootstrap percolation in a random subhypergraph. Contributed conference session talk, 2017. Random Structures and Algorithms (RS&A), Gniezno.
32. The Best Way to Spread a Rumour in a High-Dimensional Grid. Invited seminar talk, 2017. Combinatorial Group Seminar, Czech Academy of Science, Prague.
33. The Best Way to Spread a Rumour in a High-Dimensional Grid. Invited seminar talk, 2017. Discrete Math Seminar, KAIST, Daejeon.
34. Bootstrap percolation in a random subhypergraph. Invited conference talk, 2017. Structure in Graphs and Matroids (SiGMa).
35. Antichains in Random Posets via Supersaturation and Containers. Invited seminar talk, 2017. Probability Seminar, Paul Sabatier University, Toulouse.
36. Supersaturation in Posets and Applications Involving the Container Method. Invited seminar talk, 2016. Mittagsseminar, ETH Zurich.
37. Reconfiguring Graph Homomorphisms and Colourings. Invited conference session talk, 2016. SIAM Conference on Discrete Mathematics (SIAM DM16), Atlanta.
38. Extremal Bounds for Bootstrap Percolation in the Hypercube. Invited seminar talk, 2016. Combinatorics Seminar, University of Birmingham.
39. Extremal Bounds for Bootstrap Percolation in the Hypercube. Invited seminar talk, 2016. Discrete Mathematics and Optimization Seminar, McGill University.
40. Extremal Bounds for Bootstrap Percolation in the Hypercube. Invited seminar talk, 2015. Graph Theory Seminar, University of West Bohemia, Pilsen.
41. Extremal Bounds for Bootstrap Percolation in the Hypercube. Invited seminar talk, 2015. Noon Lecture, Charles University, Prague.
42. Choosability of Graphs With Bounded Order. Invited seminar talk, 2014. Combinatorics Seminar, University of Warwick.
43. Choosability of Graphs With Bounded Order. Invited conference session talk, 2014. SIAM Conference on Discrete Mathematics (SIAM DM14), Minneapolis.
44. List Colourings of Graphs on a Bounded Number of Vertices. Contributed conference session talk, 2014. Summit:240, Budapest.
45. Choosability of Graphs With Bounded Order. Invited seminar talk, 2013. Mathematics Seminar, Thompson Rivers University.
46. Choosability of Graphs With Bounded Order. Invited seminar talk, 2013. Noon Lecture, Charles University, Prague.
47. Choosability of Graphs With Bounded Order. Invited seminar talk, 2013. Discrete Math Seminar, Simon Fraser University.
48. Choosability of Graphs With Bounded Order. Contributed conference talk, 2013. Seventh Czech-Slovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications, Košice.
49. Choosability of Graphs With Bounded Order. Invited seminar talk, 2012. Zhejiang Normal University, Jinhua.
50. Choosability of Graphs With Bounded Order. Contributed conference talk, 2012. Thailand-Japan Joint Conference on Computational Geometry and Graphs (TJJCCGG), Bangkok.
51. Choosability of Graphs With Bounded Order. Invited seminar talk, 2012. South China Normal University, Guangzhou.
52. Choosability of Graphs With Bounded Order. Invited seminar talk, 2012. Kyoto University, Kyoto.
53. Choosability of Graphs With Bounded Order. Invited seminar talk, 2012. Keio University, Yokohama.
54. Choosability of Graphs With Bounded Order. Invited seminar talk, 2012. National Institute of Pure and Applied Mathematics (IMPA), Rio de Janeiro.

If you would like to apply to be a graduate student at UVic, then please take careful note of the deadlines. Applications sometimes take weeks or months to go through the internal UVic system before professors can see them, and some arrive so late that faculty do not see them until after decisions have been made. This is especially common for international applicants.

I therefore strongly recommend applying as early as possible — ideally weeks or even months before the deadline. After you submit your application through the UVic system, I also recommend emailing it directly to any potential supervisor(s). That is the only reliable way to ensure they have actually seen it.

All PhD students in the department must pass candidacy before formally beginning research. However, if you do a PhD with me, we will start doing research as soon as you are ready, which may be well before you have completed candidacy. I will do my best to help design a candidacy plan that supports your longer-term goals.

General Advice

• Gian-Carlo Rota — Ten Lessons I Wish I Had Been Taught
• Advice to a Young Mathematician with contributions from Sir Michael Atiyah, Béla Bollobás, Alain Connes, Dusa McDuff, and Peter Sarnak.
• Terence Tao — Career Advice
• Fan Chung — advice for grad students
• William P. Thurston — On Proof and Progress in Mathematics
• Guidance for graduate students, new PhDs, and professionals at all levels from the Committee on the Status of Women in Computing Research
• Sarah Billey’s advice page
• Specific information for UVic math graduate students can be found on the Guidelines page on the UVic Math & Stats Department site. In particular, I suggest reading the Graduate Handbook .

Writing and Presenting Mathematics

• Paul Halmos — How to Write Mathematics and How to Talk Mathematics
• Donald E. Knuth, Tracy Larrabee and Paul M. Roberts — Mathematical Writing
• Keith Conrad — Advice on mathematical writing
• Stephen G. Krantz — How to Write Your First Paper
• John Etnyre — The Art of Writing Introductions
• Francis Su — Guidelines for good mathematical writing
• Agelos Georgakopoulos — How to give a good talk
• Bruce C. Berndt — How to write mathematical papers
• Chris Godsil — Advice on how to write well and give good talks
• Doug West — The Grammar According to West
• Terence Tao — On Writing
• Tim Gowers — How mathematics should be taught to non-mathematicians

A popular way of presenting scientific results is through a poster session. Unfortunately, most posters are impossible to learn anything from. If you would like your poster to not suck, I recommend Mike Morrison’s two videos and the following poster templates.

Other Advice

• Familiarize yourself with the types of questions that one is asked during a PhD, postdoc or faculty position interview and practice answering them. I have started to compile a list of possible interview questions for jobs in mathematics that you may find helpful.
• I recommend all students and early career researchers in discrete mathematics subscribe to the Discrete Mathematics and Algorithms Network (DMANET) mailing list .
• I also recommend subscribing to the math.CO arXiv mailing list to keep yourself up to date on the latest developments in the area.
• It is important for early career researchers to have an academic webpage. This still applies if you have only a few papers, or none at all. It is crucial that people can easily find out (a) who you are, (b) where you are, (c) what you’re interested in, and (d) what you’ve done. You do not want to miss out on opportunities just because people cannot find you.
• Go to conferences and give talks. It is a great way to meet new people in the area, get exposure to new ideas and disseminate your work. Doug West maintains a comprehensive list of conferences in combinatorics. See also the CanaDAM Discrete Mathematics Conference Directory.

Equity, Diversity and Inclusion

Members of underrepresented groups face special obstacles in the mathematical sciences, and in academia more broadly. Mathematics, and academia as a whole, is still in the process of understanding and recognizing these challenges and learning how to overcome them, but some great progress is being made by some amazing people. For more information:

• The Math is For All project created by Annie Raymond; see also the Instagram.
• Lathisms: Latinxs and Hispanics in the Mathematical Sciences
• Indigenous Mathematicians
• Mathematically Gifted and Black
• National Association of Mathematicians
• Mathematicians of the African Diaspora
• Meet a Mathematician
• Association for Women in Mathematics UVic Student Chapter
• UVic’s Policy on Human Rights, Equity and Fairness
• Math & Statistics Equity, Diversity and Inclusion (MSEDI) committee at UVic
• NSERC’s guide for applicants on considering equity, diversity and inclusion
• LMS advice on diversity at conferences and seminars

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Undergraduate Research

• NSERC Undergraduate Student Research Awards (USRA) ; see also the UVic Math & Stats undergraduate research page .
• UVic Science Undergraduate Research Awards (SURA)
• UVic Jamie Cassels Undergraduate Research Awards (JCURA)
• UVic Valerie Kuehne Undergraduate Research Awards (VKURA)
• Mitacs Globalink Research Awards provide funding for senior undergraduates, graduate students and postdocs to undertake a 12–24 week research project in another country.

Undergraduate Travel Funding

• UVic Boehm Family Award for Undergraduate Travel

International Undergraduate Research Internships

• Mitacs Globalink Research Internship

Undergraduate Activities

• Canadian Mathematics Society Student Committee Student Activities Funding Application

Graduate Student Funding (Master’s and PhD)

• NSERC Postgraduate Scholarships and Canada Graduate Scholarships (PGS / CGS M and D) (Canadian citizens and permanent residents only)
• NSERC Vanier Canada Graduate Scholarships
• Eiffel Scholarship
• Jane Street Graduate Research Fellowships
• More information about funding opportunities for grad students can be found on the UVic Math & Stats Financial Support page .

Graduate Student Travel Funding

• Faculty of Graduate Studies travel grants at UVic
• CUPE 4163 conference funding
• Mitacs Globalink Research Awards
• Many conferences offer travel funding for students. For students in combinatorics, the SIAM Discrete Math conference (held in even years) and the CanaDAM conference (held in odd years) usually do. If you want to get travel funding, then you should probably plan to present a talk.

Postdoctoral Fellowships

• PIMS Postdoctoral Fellowships
• CRM Postdoctoral Fellowships
• Fields Research Fellowships
• NSERC Postdoctoral Fellowships
• NSERC Banting Postdoctoral Fellowships
• PIMS/CNRS Postdoctoral Fellowships
• Marie Skłodowska-Curie Postdoctoral Fellowships
• Leverhulme Early Career Fellowships
• Research Fellowships from the Royal Commission for the Exhibition of 1851
• Royal Society University Research Fellowships
• Heilbronn Research Fellowships
• Humboldt Research Fellowships
• Warwick Zeeman Lecturer
• Junior Research Fellowships at Oxford and Cambridge colleges
• Imperial Research Fellowships
• Dirichlet Postdoctoral Fellowships
• Dorothy Hodgkin Fellowships
• Czech Science Foundation Postdoc Individual Fellowships

Job Boards

• mathjobs.org
• jobs.ac.uk
• European Mathematical Society job listings
• MathHire.org
• AWM Job Board

Postdoc Travel Funding

• Mitacs Globalink Research Awards
• Many conferences offer travel funding for students and postdocs. In combinatorics, the SIAM Discrete Math conference and the CanaDAM conference are especially relevant.