The LSE Mathematics Department has a strong group working in various topics in Discrete Mathematics, especially algorithmic aspects. The interface between Theoretical Computer Science and Discrete Mathematics has been highlighted by recent EPSRC Reviews of both disciplines as being one of increasing importance, and LSE is well placed to be at the forefront of future developments.
Peter Allen: Extremal and random combinatorics; in particular Ramsey theory, extremal (hyper)graph theory, extremal theorems on (quasi)random structures, and algorithmic aspects thereof.
Martin Anthony: Mathematical aspects of machine learning, particularly probabilistic modelling of learning and discrete mathematical problems in the theory of learning, data mining and artificial neural networks; Boolean function classes and their representations.
Tugkan Batu: Algorithms and theory of computation; particularly, randomized computation, sublinear algorithms on massive data sets, property testing, computational statistics.
Julia Boettcher: Extremal combinatorics, random and quasi-random discrete structures, Ramsey theory, algorithmical and structural graph theory, graph colouring.
Graham Brightwell: Combinatorics in general, especially finite partially ordered sets, probabilistic methods, and algorithmic aspects.
Jan van den Heuvel: Discrete mathematics in general; graph theory; matroid theory; applications and algorithmic aspects of graph theory; mathematical aspects of frequency assignment problems; mathematical aspects of networks.
Jozef Skokan: Extremal set theory, quasi-random structures, probabilistic combinatorics, discrete geometry, graph theory, combinatorial games and topics in theoretical computer science.
Konrad Swanepoel: Combinatorial and Discrete Geometry; Axiomatic Geometry; Finite Geometries; Geometry of finite-dimensional Normed Spaces; Geometric shortest networks, such as Steiner Minimal Trees and the Fermat-Torricelli Problem; Extremal Combinatorics.