HELLO
Welcome, bem vindo, bienvenue...
I am an Assistant 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 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.
To appear
Spanning trees in pseudorandom graphs via sorting networks
With Joseph Hyde, Alp Müyesser, and Matías Pavez-Signé
(Also mentioned here.)
On uncommon systems of equations With Nina Kamčev and Anita Liebenau
Off-Diagonal Commonality of Graphs via Entropy
With Natalie Behague and Jonathan Noel
On multicolor Turán numbers
With József Balogh, Anita Liebenau, and Letícia Mattos
Submitted
Thresholds for constrained Ramsey and anti-Ramsey problems
Natalie Behague, Robert Hancock, Joseph Hyde, and Shoham Letzter
Generalized Ramsey numbers via conflict-free hypergraph matchings
With Andrew Lane
An Approximate Counting Version of the Multidimensional Szemerédi Theorem
With Natalie Behague, Joseph Hyde, Jonathan Noel, and Ashna Wright
Common Pairs of Graphs
With Natalie Behague and Jonathan Noel
Layered subgraphs of the hypercube
With Natalie Behague, Imre Leader, and Kada Williams
A note on the invertibility of oriented graphs
With Natalie Behague, Tom Johnston, and Shannon Ogden
Published
Directed cycles with zero weight in ℤpk
Journal of Combinatorial Theory. Series B (2024) With Shoham Letzter
The rainbow saturation number is linear
SIAM Journal on Discrete Mathematics (2024) With Natalie Behague, Tom Johnston, Shoham Letzter, and Shannon Ogden
Improved bounds for cross-Sperner systems
Electronic Journal of Combinatorics (2024) With Natalie Behague, Akina Kuperus, and Ashna Wright
Towards a characterisation of Sidorenko systems
The Quarterly Journal of Mathematics (2023) With Nina Kamčev and Anita Liebenau
Every graph is eventually Turán-good
Journal of Combinatorial Theory. Series B (2023) With JD Nir, Sergey Norin, Paweł Rzążewski, and Alexandra Wesolek
The typical structure of sets with small sumset
International Mathematics Research Notices. IMRN (2022) With Marcelo Campos, Maurício Collares, Rob Morris, and Victor Souza
On the singularity of random symmetric matrices
Duke Mathematical Journal (2021) With Marcelo Campos, Letícia Mattos and Rob Morris
Lagrangians of Hypergraphs II: When colex is best
Israel Journal of Mathematics (2021) With Vytautas Gruslys and Shoham Letzter
A Sharp Threshold for Bootstrap Percolation in a Random Hypergraph
Electronic Journal of Probability (2021) With Jonathan Noel
Maximising the Number of Cycles in Graphs with Forbidden Subgraphs
Journal of Combinatorial Theory. Series B (2021) With Alex Roberts and Alex Scott
Weak saturation numbers of complete bipartite graphs in the clique
Journal of Combinatorial Theory. Series A (2021) With Gal Kronenberg and Taísa Martins
Bounding the number of cycles in a graph in terms of its degree sequence
European Journal of Combinatorics (2021) With Zdeněk Dvořák, Jonathan Noel, Sergey Norin, and Luke Postle
Hypergraph Lagrangians I: the Frankl-Füredi conjecture is false
Advances in Mathematics (2020) With Vytautas Gruslys and Shoham Letzter
The Kőnig Graph Process
Random Structures & Algorithms (2020) With Nina Kamčev, Michael Krivelevich, and Benny Sudakov
Partitioning the vertices of a torus into isomorphic subgraphs
Journal of Combinatorial Theory. Series A (2020) With Marthe Bonamy and Alex Scott
The size-Ramsey number of powers of paths
Journal of Graph Theory (2019) With Dennis Clemens, Matthew Jenssen, Yoshiharu Kohayakawa, Guilherme Oliveira Mota, Damian Reding, and Barnaby Roberts
Extremal Bounds for Bootstrap Percolation in the Hypercube
Journal of Combinatorial Theory. Series A (2018) With Jonathan Noel
Maximising the number of induced cycles in a graph
Journal of Combinatorial Theory. Series B (2017) With Alex Scott
Saturation in the hypercube and bootstrap percolation
Combinatorics, Probability and Computing (2017) With Jonathan Noel and Alex Scott
Bounding the number of hyperedges in friendship r-hypergraphs
European Journal of Combinatorics (2016) With Karen Gunderson and Jason Semeraro
On saturated k-Sperner systems
Electronic Journal of Combinatorics (2014) With Jonathan Noel and Alex Scott
COLLABORATORS
Natalie Behague (x8), József Balogh (x1), Marthe Bonamy (x1), Marcelo Campos (x2), Dennis Clemens (x1), Maurício Collares (x1), Zdeněk Dvořák (x1), Vytautas Gruslys (x2), Karen Gunderson (x1), Robert Hancock (x3), Joseph Hyde (x3), Matthew Jenssen (x1), Tom Johnston (x2), Nina Kamčev (x3), Yoshiharu Kohayakawa (x1), Michael Krivelevich (x1), Gal Kronenberg (x1), Akina Kuperus (x1), Andrew Lane (x1), Imre Leader (x1), Shoham Letzter (x5), Anita Liebenau (x3), Taísa Martins (x1), Letícia Mattos (x2), Rob Morris (x2), Alp Müyesser (x1), Shannon Ogden (x2), Guilherme Oliveira Mota (x1), JD Nir (x1), Jonathan Noel (x8), Sergey Norin (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
Joseph Hyde (08/22- 06/24) Now a postdoc of Matthew Jenssen at King's College London
Natalie Behague (01/22- 10/23) Now a postdoc of Richard Montgomery at the University of Warwick
PhD Students
Shannon Ogden (09/23 - present)
Master's Students
Ashna Wright (09/22 - present) 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
Haley Freigang (05/25 - present) Andrew Lane (05/22 - present) 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