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The Department has a strong faculty 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. LSE is well placed to be at the forefront of future developments.

Individual faculty interests are listed below.

- Extremal and random combinatorics; in particular Ramsey theory
- Extremal (hyper)graph theory
- Extremal theorems on (quasi)random structures, and algorithmic aspects thereof

- 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

- Algorithms and theory of computation; particularly randomized computation
- Sublinear algorithms on massive data sets
- Property testing
- Computational statistics

- Extremal combinatorics
- Random and quasi-random discrete structures
- Ramsey theory
- Algorithmical and structural graph theory
- Graph colouring

- Combinatorics in general, especially finite partially ordered sets, probabilistic methods, and algorithmic aspects
- Random graphs
- Random structures

- Graph theory
- Matroid theory
- Applications and algorithmic aspects of graph theory
- Mathematical aspects of frequency assignment problems
- Mathematical aspects of networks
- Discrete mathematics in general

- Algorithmic processes
- Randomness
- Computability
- Algorithmic game theory
- Agent based models
- Networks
- Discrete mathematics in general

- Finite group theory
- Groups of Lie type
- Geometric group theory
- Combinatorics
- Generation of finite simple groups

- Measure theory
- Ergodic theory
- Functional analysis
- Stochastic processes
- Chaos Theory
- Combinatorics
- Algebraic topology

- Extremal set theory
- Quasi-random structures
- Probabilistic combinatorics
- Discrete geometry
- Graph theory
- Combinatorial games
- Topics in theoretical computer science

- 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

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