Dr Andrew Treglown PhD

Dr Andrew Treglown

School of Mathematics
Senior Lecturer

Contact details

Address
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Dr Andrew Treglown is a Senior Lecturer, 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 graph theory.

Andrew has a number of international collaborative links, particularly with various institutions in the USA. He regularly gives talks at international conferences and has been invited to give a number of seminars across Europe and in the USA.

For more information, please see Andrew's School of Mathematics staff profile

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.

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. In recent years his work has had a particular focus on ‘independent set’ problems in the setting of graphs, posets and the integers. This work has been supported by an EPSRC Fellowship (2015-2018). He also has interests in extremal and probabilistic combinatorics, and Ramsey theory.

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 theoretical approach, Andrew and his co-authors (J. Balogh, H. Liu and M. Sharifzadeh) gave a solution to this important question.

Much of Andrew’s recent work also considers questions in Ramsey theory. Together with his PhD student R. Hancock, and K. Staden, he generalised the random Ramsey theorem of Rödl and Ruciński by providing a resilience analogue. They also resolved a general subcase of the asymmetric random Ramsey conjecture of Kohayakawa and Kreuter.

One of the most central results in Ramsey theory is Goodman’s theorem from 1959 which determines the minimum number of monochromatic triangles in a 2-coloured complete graph. Andrew and his co-authors (J. Cummings, D. Kral, F. Pfender, K. Sperfeld and M. Young) have solved this problem for 3-coloured graphs, thereby solving a classical problem of Goodman.

In the past Andrew has made progress on a number of problems concerning graph decompositions. In particular, together with B. Csaba, D. Kühn, A. Lo and D. Osthus, he has solved the beautiful 1-factorization conjecture for large graphs. This classical conjecture gives a condition for a regular graph to have a decomposition into perfect matchings.

Andrew has also written a number of papers on (hyper)graph embedding problems. For example, in a sequence of several papers, he and his co-authors (D. Kühn, D. Osthus and Y. Zhao) have established a number of minimum 

Publications

For a complete list of publications, please visit Andrew's School of Mathematics staff profile

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