Dr Andrew Treglown MSci PhD

Dr Andrew Treglown

School of Mathematics
Associate Professor

Contact details

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

Dr Andrew Treglown is an Associate Professor, 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 2

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, Csaba, B, Pluhar, A & Treglown, A 2021, 'A discrepancy version of the Hajnal-Szemerédi theorem', Combinatorics, Probability and Computing, vol. 30, no. 3, pp. 444-459. https://doi.org/10.1017/S0963548320000516

Freschi, A, Hyde, J, Lada, J & Treglown, A 2021, 'A note on color-bias Hamilton cycles in dense graphs', SIAM Journal on Discrete Mathematics, vol. 35, no. 2, pp. 970-975. https://doi.org/10.1137/20M1378983

Hancock, R & Treglown, A 2021, 'An asymmetric random Rado theorem for single equations: the 0-statement', Random Structures and Algorithms. https://doi.org/10.1002/rsa.21039

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 2021, 'On deficiency problems for graphs', Combinatorics, Probability and Computing. https://doi.org/10.1017/S0963548321000389

Han, J, Morris, P & Treglown, A 2021, 'Tilings in randomly perturbed graphs: bridging the gap between Hajnal-Szemerédi and Johansson-Kahn-Vu', Random Structures and Algorithms, vol. 58, no. 3, pp. 480-516. https://doi.org/10.1002/rsa.20981

DeBiasio, L, Lo, A, Molla, T & Treglown, A 2021, 'Transitive tournament tilings in oriented graphs with large minimum total degree', SIAM Journal on Discrete Mathematics, vol. 35, no. 1, pp. 250–266. https://doi.org/10.1137/19M1269257

Hyde, J & Treglown, A 2020, 'A degree sequence version of the Kühn-Osthus tiling theorem', The Electronic Journal of Combinatorics, vol. 27, no. 3, #P3.48.

Falgas-Ravry, V, Markstrom, K, Treglown, A & Zhao, Y 2020, 'Existence thresholds and Ramsey properties of random posets', Random Structures and Algorithms, vol. 57, no. 4, pp. 1097-1133. https://doi.org/10.1002/rsa.20952

Das, S & Treglown, A 2020, 'Ramsey properties of randomly perturbed graphs: cliques and cycles', Combinatorics, Probability and Computing, vol. 29, no. 6, pp. 830-867. https://doi.org/10.1017/S0963548320000231

Staden, K & Treglown, A 2020, 'The bandwidth theorem for locally dense graphs', Forum of Mathematics, Sigma, vol. 8, e42. https://doi.org/10.1017/fms.2020.39

Han, J & Treglown, A 2020, 'The complexity of perfect matchings and packings in dense hypergraphs', Journal of Combinatorial Theory. Series B, vol. 141, pp. 72-104. https://doi.org/10.1016/j.jctb.2019.06.004

Das, S, Morris, P & Treglown, A 2020, 'Vertex Ramsey properties of randomly perturbed graphs', Random Structures and Algorithms, vol. 57, no. 4, pp. 983-1006. https://doi.org/10.1002/rsa.20971

Hyde, J, Liu, H & Treglown, A 2019, 'A degree sequence Komlós theorem', SIAM Journal on Discrete Mathematics, vol. 33, no. 4. https://doi.org/10.1137/18M1197102

Hancock, R, Staden, K & Treglown, A 2019, 'Independent sets in hypergraphs and Ramsey properties of graphs and the integers', SIAM Journal on Discrete Mathematics, vol. 33, no. 1, pp. 153-188. https://doi.org/10.1137/18M119642X

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