Course summary

For more information about the School and the research programmes please see School of Mathematical Sciences School's research groups: Algebra and Number Theory Combinatorics Complex Systems and Networks Dynamical Systems and Statistical Physics Geometry and Analysis Probability and Applications Algebra and Number Theory The Algebra and Number Theory Group at QMUL has a long and distinguished history, going back to such names as Kurt Hirsch, Karl Gruenberg and Ian G. Macdonald. Having made its reputation primarily in group theory, it now covers a range of areas in group theory, representation theory, number theory, algebraic combinatorics, algebraic geometry, logic, homological/categorical algebra, and computational methods. Combinatorics A very active group that works both on topics within combinatorics (especially finite geometry and design theory) and on links with algebra (permutation groups), logic (model theory), information and coding theory, and design of experiments. Complex Systems and Networks The Complex Systems and Networks group is interested in the mathematical description and modelling of the architecture and dynamics of complex systems. Its main goal is to understand how a complex system self-organizes and how various collective behaviours emerge when a large number of units or dynamical systems interact through non-trivial networks. It makes use of mathematical tools from graph theory, statistical mechanics and nonlinear dynamics, and large-scale numerical simulations. The group is interested in applications to biology, social systems, and man-made networks, where it address both fundamental problems as well as applied research with some industrial collaborators. Dynamical Systems and Statistical Physics The Dynamical Systems and Statistical Physics Group has a broad range of research interests in the area of statistical mechanics as applied to a variety of complex systems, and in the mathematical foundations of dynamical systems theory. Particular emphasis is on non-equilibrium processes, stochastic modelling, ergodic theory, chaotic and nonlinear phenomena, and interdisciplinary applications. The group has numerous collaborations and links with other groups in the department, and with other research groups worldwide. Geometry and Analysis The Geometry and Analysis group a vibrant research group with expertise in algebraic, differential and noncommutative geometry, functional and harmonic analysis, mathematical relativity theory, model theory, operator algebras, partial differential equations, quantum algebra and topology. It organises regular seminars throughout the academic year and works closely with other groups in the School of Mathematical Sciences: Algebra, Combinatorics, Dynamical Systems and Statistical Physics. Probability and Applications Probability is both a fundamental way of viewing the world, and a core area of mathematics. Probability theory is concerned with the analysis of mathematical models of random phenomena, as occur in many branches of science. The group Probability and Applications at QMUL is engaged in numerous research activities, including stochastic processes, statistics, random discrete structures, random matrices and stochastic optimisation, as well as in applications of probability to statistical physics, modelling of epidemics, networks, financial engineering and other areas.