The main research interests of our group lie in combinatorics, the study of random discrete structures and the analysis of randomized algorithms.
Combinatorial structures of particular interest are graphs and hypergraphs. Indeed, large graphs underpin much of modern society and science, and can be used to model networks in biology, sociology or computer science. These models give rise to a variety of challenging computational problems. The probabilistic perspective arises both as an invaluable method of proof as well as through the analysis of typical properties of combinatorial objects.
For more information see the Combinatorics, Probability and Algorithms in Birmingham page.
Head of Combinatorics Group
Senior Lecturer
Dr Lo's research interests lie in Extremal and Probabilistic Graph Theory. A typical problem in this field is to determine the necessary conditions for the existence of a fixed spanning subgraph in a graph, edge-coloured graph, orientated graph or hypergraph.
Academic Staff
Reader and Senior Birmingham Fellow
Dr Carmesin is working at the interface of Combinatorics and Topology. He is particularly interested in Graph Minors, Connectivity and Matroids. Recently he characterised the simply connected 2-complexes embeddable in 3-space - in a way similar to Kuratowski's characterisation of graph planarity.
Reader in Probabilistic Combinatorics
Dr Fountoulakis's interests are mainly around random discrete structures and the analysis of random processes on graphs, and connections with computer science and average-case analysis. Recently he worked on the development of the theory of random graphs on the hyperbolic plane and applications to complex networks. He is also interested in percolation phenomena in large finite structures.
Professor in Mathematics (Mason Chair)
Professor Kühn's research interests lie mainly in Extremal and Probabilistic Combinatorics, as well as algorithmic applications. In particular, she used probabilistic methods to solve several problems on Hamilton cycles in graphs and digraphs, graph decompositions and hypergraph matchings.
Lecturer in Combinatorics
Dr Long's research interests lie in extremal and probabilistic combinatorics, with a emphasis on extremal set theory, graph theory, probabilistic methods in combinatorics, and high-dimensional phenomena. Recently his work has focused on discrete isoperimetric inequalities, graph Ramsey theory and intersection theorems for finite sets.
Senior Lecturer
Dr Mycroft's research is primarily in the field of extremal graph theory. Recent results include general sufficient conditions which ensure the existence of perfect matchings and Hamilton cycles in hypergraphs, or which permit the construction of efficient algorithms to find such structures (should they exist).
Professor in Graph Theory
Professor Osthus's research interests are in extremal graph theory, random graphs, randomized algorithms, structural graph theory as well as Ramsey theory. His recent research has included results on Hamilton cycles and more general spanning substructures, as well as decompositions of graphs and hypergraphs.
Professor of Mathematics
Professor Treglown's primary research interests lie in Extremal and Probabilistic Combinatorics as well as in Ramsey Theory and Combinatorial Number Theory. He is also interested in graph decompositions and on a number of embedding problems in the directed graph and hypergraph setting.
Research and Teaching Fellows
Research Fellow
Ms Boyadzhiyska's main field of interest in Ramsey theory, but she enjoys working on problems from other areas of combinatorics as well. She has worked on problems related to minimum degrees of minimal Ramsey graphs, Ramsey equivalence, orthogonal Latin squares, and grid coverings.
Research Fellow
Miss Kathapurkar's research interests lie in extremal and probabilistic combinatorics.
Research Fellow
Dr Kurkofka's research interests include graph minors, connectivity, graph-decompositions, graph coverings and 3D combinatorics. He has also studied the combinatorial and topological aspects of infinite graphs, with the overarching aim of better understanding the structure of infinite graphs.
Research Fellow in Combinatorics
Mr Pfenninger's research is on extremal and probabilistic combinatorics, graph and hypergraph theory, Ramsey theory, monochromatic cycle partitions, Lehel's conjecture and extremal set theory.
Research Fellow
Dr Piga is interested in extremal and probabilistic combinatorics, especially in problems for hypergraphs and finite sets.
PhD Students
Note that not all PhD researchers have requested profiles.