HELLO
Welcome, bem vindo, bienvenue...
I am an Associate Professor at the University of Victoria in Canada. Before this, I was a Research Fellow in Mathematics at Sidney Sussex College in Cambridge, UK. I was also a Postdoctoral Research Fellow (under the supervision of Rob Morris) at IMPA in Rio de Janeiro, Brazil. I obtained my PhD in 2018 from the University of Oxford under the supervision of Alex Scott. Before coming to Oxford, I did Part III of the Mathematical Tripos at Cambridge (also at Sidney!) and I completed my undergraduate studies at University College, Durham.
I have a wide range of research interests, mainly in the areas of extremal and probabilistic combinatorics. In particular, I am interested in extremal graph theory, random graphs and processes, graph colouring, bootstrap percolation and related cellular automata, and Ramsey Theory. Having said that, I am always interested in hearing about new problems to work on and meeting new people to work with (my email address can be found here). My research papers can be found here.
For some articles on my research, see here (University of Cambridge) or here (IMPA - em português).
If this section has failed to tell you sufficiently about me, try here for some more non-mathematical information.
RESEARCH PAPERS
A link to my papers on arXiv can be found here.
Published
An approximate counting version of the multidimensional Szemerédi theorem
Combinatorica 45 (2025)
With Natalie Behague, Joseph Hyde, Jonathan A. Noel, and Ashna Wright
Thresholds for constrained Ramsey and anti‑Ramsey problems
European Journal of Combinatorics 129 (2025)
With Natalie Behague, Robert Hancock, Joseph Hyde, and Shoham Letzter
Spanning trees in pseudorandom graphs via sorting networks
Proceedings of the American Mathematical Society 153 (2025)
With Joseph Hyde, Alp Müyesser, and Matías Pavez‑Signé
A note on inverting the dijoin of oriented graphs
Electronic Journal of Combinatorics 32 (2025)
With Natalie Behague, Tom Johnston, and Shannon Ogden
Common Pairs of Graphs
Combinatorics, Probability, and Computing 34 (2025)
With Natalie Behague and Jonathan A. Noel
On uncommon systems of equations
Israel Journal of Mathematics 264 (2024)
With Nina Kamčev and Anita Liebenau
Layered subgraphs of the hypercube
Electronic Journal of Combinatorics 31 (2024)
With Natalie Behague, Imre Leader, and Kada Williams
Off‑diagonal commonality of graphs via entropy
SIAM Journal on Discrete Mathematics 38 (2024)
With Natalie Behague and Jonathan A. Noel
On multicolor Turán numbers
SIAM Journal on Discrete Mathematics 38 (2024)
With József Balogh, Anita Liebenau, and Letícia Mattos
Directed cycles with zero weight in ℤpk
Journal of Combinatorial Theory, Series B 168 (2024)
With Shoham Letzter
Improved bounds for cross‑Sperner systems
Electronic Journal of Combinatorics 31 (2024)
With Natalie Behague, Akina Kuperus, and Ashna Wright
The rainbow saturation number is linear
SIAM Journal on Discrete Mathematics 38 (2024)
With Natalie Behague, Tom Johnston, Shoham Letzter, and Shannon Ogden
Towards a characterization of Sidorenko systems
The Quarterly Journal of Mathematics 74 (2023)
With Nina Kamčev and Anita Liebenau
Every graph is eventually Turán‑good
Journal of Combinatorial Theory, Series B 162 (2023)
With JD Nir, Sergey Norin, Paweł Rzążewski, and Alexandra Wesolek
Weak saturation numbers of complete bipartite graphs in the clique
Journal of Combinatorial Theory, Series A 178 (2021)
With Gal Kronenberg and Taísa Martins
On the singularity of random symmetric matrices
Duke Mathematical Journal 170 (2021)
With Marcelo Campos, Letícia Mattos, and Rob Morris
The typical structure of sets with small sumset
International Mathematics Research Notices IMRN (2022)
With Marcelo Campos, Maurício Collares, Rob Morris, and Victor Souza
A Sharp Threshold for Bootstrap Percolation in a Random Hypergraph
Electronic Journal of Probability 26 (2021)
With J.A. Noel
Lagrangians of hypergraphs II: When colex is best
Israel Journal of Mathematics 242 (2021)
With Vytautas Gruslys and Shoham Letzter
Maximising the number of cycles in graphs with forbidden subgraphs
Journal of Combinatorial Theory, Series B 147 (2021)
With Alex Roberts and Alex Scott
Bounding the number of cycles in a graph in terms of its degree sequence
European Journal of Combinatorics 91 (2021)
With Zdeněk Dvořák, Jonathan A. Noel, Sergey Norin, and Luke Postle
Hypergraph Lagrangians I: The Frankl‑Füredi conjecture is false
Advances in Mathematics 365 (2020)
With V. Gruslys and S. Letzter
The Kőnig Graph Process
Random Structures & Algorithms 57 (2020)
With N. Kamčev, M. Krivelevich, and B. Sudakov
Partitioning the vertices of a torus into isomorphic subgraphs
Journal of Combinatorial Theory, Series A 174 (2020)
With M. Bonamy and A. Scott
The size‑Ramsey number of powers of paths
Journal of Graph Theory 91(3) (2019)
With D. Clemens, M. Jenssen, Y. Kohayakawa, G. Mota, D. Reding, and B. Roberts
Extremal bounds for bootstrap percolation in the hypercube
Journal of Combinatorial Theory, Series A 156 (2018)
With J. A. Noel
Maximising the number of induced cycles in a graph
Journal of Combinatorial Theory, Series B 126 (2017)
With A. Scott
Saturation in the hypercube and bootstrap percolation
Combinatorics, Probability and Computing 26(1) (2017)
With J. A. Noel and A. Scott
Bounding the number of hyperedges in friendship r‑hypergraphs
European Journal of Combinatorics 51 (2016)
With K. Gunderson and J. Semeraro
On saturated k‑Sperner systems
Electronic Journal of Combinatorics 21 (2014)
With J. A. Noel and A. Scott
Submitted
Perfect tilings of 3-graphs with the generalised triangle
With C. Bowtell and R. Mycroft
Universality for transversal powers of Hamilton cycles
With E. Heath, J. Hyde, and S. Ogden
Generalized Ramsey numbers via conflict-free hypergraph matchings
With A. Lane
Using polynomials to find lower bounds for r-bond bootstrap percolation
With S. Ogden
Improved bounds for proper rainbow saturation
With A. Lane
Proper rainbow saturation for trees
With A. Lane
Infinite induced-saturated graphs
With M. Bonamy, C. Groenland, T. Johnston, and A. Scott
COLLABORATORS
József Balogh (x1) Natalie Behague (x8) Marthe Bonamy (x2) Candida Bowtell (x1) Marcelo Campos (x2) Maurício Collares (x1) Dennis Clemens (x1) Zdeněk Dvořák (x1) Carla Groenland (x1) Vytautas Gruslys (x2) Karen Gunderson (x1) Robert Hancock (x1) Emily Heath (x1) Joseph Hyde (x4) Imre Leader (x1) Matthew Jenssen (x1) Tom Johnston (x3) Nina Kamčev (x3) Yoshiharu Kohayakawa (x1) Michael Krivelevich (x1) Gal Kronenberg (x1) Akina Kuperus (x1) Andrew Lane (x3) Shoham Letzter (x5) Anita Liebenau (x3), Taísa Martins (x1), Letícia Mattos (x2), Rob Morris (x2) Guilherme Mota (x1) Alp Müyesser (x1), Richard Mycroft (x1), JD Nir (x1), Jonathan Noel (x8), Sergey Norin (x2), Shannon Ogden (x2), Matías Pavez-Signé (x1), Luke Postle (x2), Damian Reding (x1), Barnaby Roberts (x1), Alex Roberts (x1), Paweł Rzążewski (x1), Alex Scott (x5), Jason Semeraro (x1), Victor Souza (x1), Benny Sudakov (x1), Alexandra Wesolek (x1), Kada Williams (x1), Ashna Wright (x2)
POSTDOCS & STUDENTS
Postdocs (co-supervised with Jon Noel)
Felix Clemen (01/25- 12/26)
Joseph Hyde (08/22- 06/24) Now a postdoc of Matthew Jenssen at King's College London
Natalie Behague (01/22- 10/23) Now an assistant professor at Dublin City University
PhD Students
Shannon Ogden (09/23 - present)
Master's Students
Joy Cooper (09/25 - present) co-supervised with Peter Dukes
Ashna Wright (09/22 - 06/24) co-supervised with Jonathan Noel
Thesis: Counting X-free sets
Shannon Ogden (09/21 - 07/23) co-supervised with Kieka Mynhardt
Thesis: Saturation Problems on Graphs
Akina Kuperus (09/21 - 07/23)
Thesis: Cross-Sperner Systems
Undergraduate Research Students
Sophie Pavlik (05/25 - 04/26) Josh Childs (09/25 - 04/26) Kira Hodge (09/24 - 04/25) Haley Freigang (05/24 - 04/25) Andrew Lane (05/22 - 12/24) Amy Penney (09/23 - 04/24) Ashna Wright (10/21 - 08/22)
If you are interested in doing research with me as a student or post-doc, please get in touch :)
CONTACT
Postcards and deliveries of delicious cheese always welcome at...
Address: David Turpin Building, 3800 Finnerty Rd, Victoria, BC V8P 5C2