Professor Andrew Treglown MSci PhD

School of Mathematics
Professor of Mathematics

Contact details

Email: a.c.treglown@bham.ac.uk

Address: School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Andrew Treglown is a Professor at the School of Mathematics, having previously worked as a Research Fellow at Queen Mary, University of London and Charles University, Prague. Andrew is a member of the Combinatorics group. His research interests mainly focus on extremal and probabilistic combinatorics and well as applications of combinatorics to other areas of mathematics. In 2021 Andrew was awarded the Fulkerson Prize jointly with his collaborators Bela Csaba, Daniela Kühn, Allan Lo and Deryk Osthus.

Personal webpage.

Qualifications

PhD in Pure Mathematics, University of Birmingham, 2011
MSci in Mathematical Sciences, University of Birmingham, 2007

Biography

Andrew Treglown received an MSci from Birmingham in 2007, followed by a PhD in 2011. After research fellowships at Queen Mary, University of London and Charles University, Prague, he re-joined the School of Mathematics here in Birmingham in September 2013.

Teaching

Semester 1

LC Vectors, Geometry and Linear Algebra

LH/LM Combinatorics and Communication Theory

Postgraduate supervision

Andrew Treglown is interested in supervising PhD students in Combinatorics. If you are interested, please email him.

Research

Research themes

Extremal graph theory
Probabilistic combinatorics
Combinatorial number theory
Ramsey theory

Research activity

Andrew's research interests lie in a range of different areas. One topic his work has had a particular focus on is 'independent set' problems in the setting of graphs, posets and the integers. This work was supported by an EPSRC Fellowship (2015-2018). For example, a famous result of Green and Sapozhenko determines the number of sum-free sets in the first n natural numbers. In the 1990s, Cameron and Erdős raised the question of how many maximal sum-free sets there are in this setting. Through a graph-theoretic approach, Andrew and his co-authors (J. Balogh, H. Liu and M. Sharifzadeh) gave a solution to this important question.

Andrew also works intensively on matching and tiling problems for graphs and hypergraphs, and is currently supported by an EPSRC-funded project on this topic. In a sequence of several papers, he and his co-authors have established a number of minimum degree conditions for forcing a perfect matching in a hypergraph, as well as generalising classical tiling results to the settings of directed and ordered graphs.

Publications

Recent publications

Article

Balogh, J, Treglown, A & Zarate Gueren, C 2024, 'A note on colour-bias perfect matchings in hypergraphs', SIAM Journal on Discrete Mathematics, vol. 38, no. 4, pp. 2543-2552. https://doi.org/10.1137/24M1637350

Araujo, I, Balogh, J, Krueger, R, Piga, S & Treglown, A 2024, 'On oriented cycles in randomly perturbed digraphs', Combinatorics, Probability and Computing, vol. 33, no. 2, pp. 157-178. https://doi.org/10.1017/S0963548323000391

Patkos, B & Treglown, A 2024, 'On some extremal and probabilistic questions for tree posets', The Electronic Journal of Combinatorics, vol. 31, no. 1, P1.19. https://doi.org/10.37236/12344

Araujo, I, Piga, S, Treglown, A & Xiang, Z 2024, 'Tiling edge-ordered graphs with monotone paths and other structures', SIAM Journal on Discrete Mathematics, vol. 38, no. 2, pp. 1808-1839. https://doi.org/10.1137/23M1572519

Freschi, A, Piga, S, Sharifzadeh, M & Treglown, A 2023, 'The induced saturation problem for posets', Combinatorial Theory, vol. 3, no. 3, 9. https://doi.org/10.5070/C63362792

Hancock, R & Treglown, A 2022, 'An asymmetric random Rado theorem for single equations: the 0-statement', Random Structures and Algorithms, vol. 60, no. 4, pp. 529-550. https://doi.org/10.1002/rsa.21039

Lo, A, Treglown, A & Zhao, Y 2022, 'Complete subgraphs in a multipartite graph', Combinatorics, Probability and Computing, vol. 31, no. 6, pp. 1092-1101. https://doi.org/10.1017/S0963548322000141

Freschi, A & Treglown, A 2022, 'Dirac-type results for tilings and coverings in ordered graphs', Forum of Mathematics, Sigma, vol. 10, pp. e104 1–41. https://doi.org/10.1017/fms.2022.92

Day, N, Falgas-Ravry, V & Treglown, A 2022, 'Extremal problems for multigraphs', Journal of Combinatorial Theory. Series B, vol. 154, pp. 1-48. https://doi.org/10.1016/j.jctb.2021.12.003

Freschi, A, Hyde, J & Treglown, A 2022, 'On deficiency problems for graphs', Combinatorics, Probability and Computing, vol. 31, no. 3, pp. 478-488. https://doi.org/10.1017/S0963548321000389

Hassler, N & Treglown, A 2022, 'On maximal sum-free sets in abelian groups', The Electronic Journal of Combinatorics, vol. 29, no. 2, P2.32, pp. 1-24. https://doi.org/10.37236/10632

Conference contribution

Freschi, A, Piga, S, Sharifzadeh, M & Treglown, A 2023, A general bound for the induced poset saturation problem. in EUROCOMB’23., 63, European Conference on Combinatorics, Graph Theory and Applications, no. 12, Masaryk University Press, pp. 1-6, European Conference on Combinatorics, Graph Theory and Applications, Prague, Czech Republic, 28/08/23. https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-063

Araujo, I, Balogh, J, Krueger, RA, Piga, S & Treglown, A 2023, Cycles of every length and orientation in randomly perturbed digraphs. in EUROCOMB’23., 9, European Conference on Combinatorics, Graph Theory and Applications, no. 12, Masaryk University Press, pp. 1-8, European Conference on Combinatorics, Graph Theory and Applications, Prague, Czech Republic, 28/08/23. https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-009

Araujo, I, Piga, S, Treglown, A & Xiang, Z 2023, Tiling problems in edge-ordered graphs. in EUROCOMB’23., 10, European Conference on Combinatorics, Graph Theory and Applications, no. 12, Masaryk University Press, pp. 1-8, European Conference on Combinatorics, Graph Theory and Applications, Prague, Czech Republic, 28/08/23. https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-010

Preprint

Freschi, A, Piga, S, Sharifzadeh, M & Treglown, A 2022 'The induced saturation problem for posets'.

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