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.
We are always keen to hear from talented students who are interested in these topics and would like to pursue PhD study in this area.


OPEN POSITIONS
Applications are invited for a Lectureship in Combinatorics and a Lectureship in Probability and Modern Statistics in the School of Mathematics at the University of Birmingham (closing date: 13th December 2018).
We strongly encourage lectureship applicants working at the interface of Combinatorics and Probability to apply for both positions.
Informal enquiries about applications are advised at an early stage and can be made to Daniela Kühn or Deryk Osthus.
We are currently advertising two Research fellowships in Combinatorics, each for two years (closing date: 5 December 2018).
One of these is funded by an EPSRC grant (PI: Deryk Osthus) and one by an EPSRC fellowship (PI: Daniela Kuhn).
The starting date is May 1 or later.
WHO ARE WE?

Daniela Kühn
Daniela'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.




Deryk Osthus
Deryk'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.


Nikolaos Fountoulakis
Nikolaos' research interests are mainly related to the area of random discrete structures and the analysis of random processes on graphs and their connections with theoretical computer science and averagecase analysis.
His most recent work has focused on the development of the theory of random graphs on the hyperbolic plane and its applications to the theory of complex networks.
He is also interested in percolation phenomena in large finite structures.




Richard Mycroft
Richard'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).


Andrew Treglown
Andrew'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.




Allan Lo
Allan'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, edgecoloured graph, orientated graph or hypergraph.


Guillem Perarnau
Guillem's main research interest is in the use of probabilistic techniques
to study both deterministic and typical properties of sparse combinatorial objects.
For instance, he has been recently working on the analysis of non classical random graphs models.




Henning Sulzbach
Henning's research interest lies in probability theory and its applications to the analysis of algorithms and random discrete structures.
His recent research focusses on branching processes, random (continuum) trees and urn models.


Johannes Carmesin
Johannes is particularly interested in Graph Minors, Connectivity and Matroids. Recently he characterised the simply connected 2complexes embeddable in 3space  in a way similar to Kuratowski's characterisation of graph planarity.




Richard Montgomery
Richard's research interests lie mainly in Extremal and Probabilistic Graph Theory. His current research themes include edgecoloured graphs
and related packing problems, and appearance thresholds in random graphs and directed graphs.
