Combinatorics, Probability and Algorithms

Combinatorial structureThe 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

Dr Johannes Carmesin

Dr Johannes Carmesin

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.

Academic Staff

Dr Nikolaos Fountoulakis

Dr Nikolaos Fountoulakis

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.

Dr Matthew Jenssen

Dr Matthew Jenssen

Lecturer in Probability and Modern Statistics
UKRI Future Leaders Fellow

Dr Jenssen's research interests include Combinatorics, Statistical Physics and their interaction with other fields. His recent research has shown how tools from Statistical Physics can be used to make progress on problems in Discrete Geometry, Ramsey Theory and Theoretical Computer Science.

Professor Daniela Kühn

Professor Daniela Kühn

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.

Dr Allan Lo

Dr Allan Lo

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.

Dr Eoin Long

Dr Eoin Long

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.

Dr Richard Mycroft

Dr Richard Mycroft

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 Deryk Osthus

Professor Deryk Osthus

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.

Dr Andrew Treglown

Dr Andrew Treglown

Associate Professor

Dr 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

Ms Simona Boyadzhiyska

Ms Simona Boyadzhiyska

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.

Miss Amarja Kathapurkar

Miss Amarja Kathapurkar

Research Fellow

Miss Kathapurkar's research interests lie in extremal and probabilistic combinatorics.

Mr Vincent Pfenninger

Mr Vincent Pfenninger

Research Fellow in Combinatorics

Vincent Pfenninger is a Research Fellow in the Combinatorics group working with Daniela Kühn and Deryk Osthus. His research interests are Extremal and Probabilistic Combinatorics.

For more information, please visit his personal webpage.

PhD Students

Note that not all PhD researchers have requested profiles.