Dr. Richard Mycroft
Lecturer in Mathematics
School of Mathematics
University of Birmingham
Birmingham B15 2TT
Watson Building, Room 322
||r.mycroft @ bham.ac.uk
ResearchMy research interests lie in the field of combinatorics, and more specifically in the area of extremal graph theory. In particular I have worked extensively on embedding problems relating to hypergraphs, centred around the development of a geometric theory of perfect matchings in uniform hypergraphs, with multiple subsequent applications both in my own work and the work of other researchers. My research project `Embeddings in Hypergraphs', supported by a £124k EPSRC First Grant, will continue this programme of research over the period 2015-17.
Aside from my work on hypergraphs, other notable results include a random version of Sperner's theorem on antichains, a multipartite version of the Hajnal-Szemerédi theorem and a proof of the longstanding Sumner's conjecture for directed trees in large tournaments.
I began my research career with PhD study at the University of Birmingham under the supervision of Deryk Osthus and co-supervised by Daniela Kühn; my doctoral thesis, submitted in 2010, was titled "The regularity method for directed graphs and hypergraphs". Following this I worked for one year as a Postdoctoral Research Assistant for Peter Keevash at Queen Mary, University of London, before returning to the University of Birmingham to take up a lectureship in June 2011.
I am currently supervising two PhD students and one MSci research project; in previous years I have supervised successful MSci research projects titled `Matchings and fractional matchings in hypergraphs' and `Hamilton Cycles in Graphs and Hypergraphs'. I am always keen to hear from talented students who would be interested in PhD research; please do get in touch if you would like further information.
Together with Daniela Kühn and Deryk Osthus I organised a workshop on Probabilistic methods in Graph Theory, which was held in March 2012. In Spring 2015 I will be the organiser of the Birmingham Combinatorics Seminar.
Since moving to Birmingham in June 2011, I have lectured the following courses:
Students taking these courses should see the course pages on Canvas for lecture notes, examples sheets and so forth.
- Autumn 2013, 2014, 2015: 1AC Combinatorics I (Year 1/2)
- Spring 2015: 3P16/4P16 Combinatorics (Year 3/4)
- Spring 2012, 2013, 2014: 2M09/3M09 Introduction to Operations Management (Year 2/3)
- Autumn 2012: 1D Discrete Mathematics (Year 1/2)
- Spring 2012: 1X Graph Colouring (Year 1)
Last updated: November 2015