I’m a third year PhD student (graduating in 2024) at University College London where I’m supervised by Alexey Pokrovskiy. Previously, I did a masters degree supervised by Tibor Szabó at Freie Universität Berlin. Before that, I was an undergraduate at Carnegie Mellon University.
I’m interested in extremal and probabilistic combinatorics, Latin squares, graph theory, and spanning subgraphs. See the Research page to see my papers. Below are some highlights.
A random Hall-Paige conjecture
with Alexey Pokrovskiy
When can we find perfect matchings in hypergraphs whose vertices represent group elements and edges represent solutions to systems of linear equations? A prototypical problem of this type is the Hall-Paige conjecture, which asks for a characterisation of the groups whose multiplication table (viewed as a Latin square) contains a transversal. Many problems in the area have a similar flavour, yet until recently they have been approached in completely different ways, using mostly algebraic tools ranging from the combinatorial Nullstellensatz to Fourier analysis. In the first paper, we give a unified approach to attack these problems, using tools from probabilistic combinatorics. In particular, we derive that a suitably randomised version of the Hall-Paige conjecture can be used as a black-box to settle many old problems in the area for sufficiently large groups. As a by-product, we obtain the first combinatorial proof of the Hall-Paige conjecture.
The second paper refines these tools further to solve a problem concerning the existence of transversals with a prescribed cycle type.
Transversal factors and spanning trees
with Richard Montgomery and Yani Pehova
Advances in Combinatorics, 2022
A general approach to transversal versions of Dirac-type theorems
with Pranshu Gupta, Fabian Hamann, Olaf Parczyk, and Amedeo Sgueglia
To appear in Bulletin of the London Mathematical Society
These papers investigate when the minimum degree threshold and the rainbow minimum degree threshold for the containment of a spanning structure are asymptotically the same. The second paper, building on tools from the first, gives a sufficient condition for when this happens. The condition (roughly speaking) is the existence of an absorption-based proof for the uncoloured version of the problem. Such absorption-based proofs are ubiquitous in the literature, hence this condition is easy to check for a large family of spanning structures. This yields rainbow versions of many classical results in extremal graph theory.
Turán‐and Ramsey‐type results for unavoidable subgraphs
with Michael Tait
Journal of Graph Theory, 2022
Unavoidable patterns in locally balanced colourings
with Nina Kamčev
To appear in Combinatorics, Probability, and Computing
Ramsey’s theorem states that any red-blue-edge-colouring of a complete graph contains a large complete subgraph which is either entirely red or entirely blue. If we add in the assumption that each colour class in the host graph is well-represented, can we strengthen Ramsey’s theorem to find a richer class of unavoidable patterns? This first paper investigates problems of this type where the host graph is non-complete. The second paper investigates the case of colourings which are locally-well-represented, in the sense that each vertex has many red and blue neighbours.