Combinatorics is the study of finite or countable discrete structures. Combinatorial problems may arise in several areas of mathematics, including algebra and probability, or in real-world applications, but they are also pursued for their own interest.

**David Ellis** and **Robert Johnson**. In addition to delicate combinatorial arguments, solutions to problems in extremal combinatorics may use tools from areas of mathematics such as representation theory and discrete Fourier analysis.

**Dudley Stark **and **Mark Walters**, who study *random structures*. For example, suppose radio transceivers with limited range are randomly scattered over an area; what is the probability that they will be able to cooperate to send messages over long distances? Or, again, what is the distribution of certain small substructures in a large random structure, for example a large random graph? To solve problems in this area one needs to combine methods from probability theory with combinatorial insights.

**Felix Fischer**’s research is concerned with problems that arise from the interaction of self-interested computationally bounded entities, or agents. His approach is mathematical and uses concepts and techniques from game theory, social choice, and mechanism design, from theoretical computer science, and from related areas of mathematics like optimization, probability theory, and graph theory. **Mark Jerrum** studies the complexity of counting problems, which even now contains some large relatively unexplored areas. A prominent emerging Leitmotiv here is the idea that phase transitions in a model in statistical physics may provably be associated with a sudden change in the complexity of computing the partition function (generating function of configurations) of the system. **Justin Ward**’s research involves the study and development of algorithms for combinatorial optimisation problems, with a focus on practical heuristics such as local search and greedy algorithms. His most recent work involves new frameworks for largescale and distributed submodular maximisation, as well as new algorithms for k-means clustering.

**Bill Jackson** considers the question: when is such a framework rigid? Although geometry often plays a part in the *theory of rigid frameworks*, there is a general setting in which the answer to the above question is purely combinatorial, i.e., is dependent only on the incidences of the bars and joints. In these cases the rigidity of a framework is determined by a related combinatorial structure called a matroid.

The Combinatorics Study Group meets on Fridays at 16:00 in Room W316 in the Queens' Building at Queen Mary University of London.

Find out more about the history of the Combinatorics Study Group here.

We also run joint colloquia with LSE - find out more here.

Lecturer in Pure Mathematics

Queens’ Building, Room: CB316

+44 (0)20 7882 3583

d.ellis@qmul.ac.uk

Lecturer in Optimisation/Operations Research

Queens’ Building W411

+44 (0)20 7882 2607

felix.fischer@qmul.ac.uk

Professor of Mathematical Sciences

Queens’ Building, Room: W410

+44 (0)20 7882 5476

b.jackson@qmul.ac.uk

Professor of Mathematics / Director of Research

Queens’ Building, Room W319

+44 (0)20 7882 5472

m.jerrum@qmul.ac.uk

Senior Lecturer in Pure Mathematics

Queens’ Building, Room: CB316

+44 (0)20 7882 5480

r.johnson@qmul.ac.uk

Postgraduate Research Student

Queens’ Building, Room: W317

t.khoployklang@qmul.ac.uk

Reader in Mathematics and Probability

Queens’ Building, Room: CB201

+44 (0)20 7882 5487

d.s.stark@qmul.ac.uk

Senior Lecturer in Pure Mathematics / Director of Education

Queens’ Building, Room: W309

+44 (0)20 7882 5446

m.walters@qmul.ac.uk

Lecturer in Optimisation/Operations Research

Queens' Building, Room W411

5065

justin.ward@qmul.ac.uk