Modern science has made clear that the reductionist viewpoint is insufficient. Even if interactions between fundamental particles are under control, new laws emerge at large, “life” scales, which are often more complex. The idea of emergence goes beyond, and systems composed of a large number of constituents in interaction, subject to hard-to-predict fluctuations, form a new theoretical paradigm for physics, biology, economy, and other disciplines. This is the ubiquitous subject of complex systems. Understanding complex systems has real-world impact, but the study of complexity also requires deep and involved mathematics, which during the years produced beautiful mathematical discoveries, such as the mean-field solution of spin glasses or the Kardar-Parisi-Zhang equation for the description of growing interfaces. In the UK there is a strong community of researchers on these and related subjects, and the Disordered Systems group of KCL’s Mathematics Department is at the forefront of research in statistical mechanics of disordered and complex systems. The group focuses its research on both fundamental problems, such as non-equilibrium systems, network theory, soft matter theory, and random matrix theory, and on applications, such as mathematical biology and quantitative medicine, social phenomena, finance, statistics and inference, machine learning.
The seminar page of the EPSRC Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems (CANES).
The Complex Systems Modelling MSc – from Biomedical & Natural to Economic & Social Sciences course will teach you to apply mathematical techniques in the rapidly developing and exciting interdisciplinary field of complex systems and examine how they apply to a variety of areas including biomedicine, nature, economics and social sciences. This research-led course is suitable for graduates who wish to work in research and development in an academic or industrial environment.
KCL Mathematics department produces excellent or world-leading research in terms of originality, significance and rigour. Join KCL for your postgraduate studies!
Last news from the group: conferences, workshops and publications
Giorgio Parisi has been awarded the 2021 Physics Nobel Prize for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales.
Izaak Neri will be a scientific coordinator of the virtual workshop organized at MPI, that aims to bring together researchers working on random matrix theory and complex systems. 7-18 June 2021. Apply!
Gioia, a CANES PhD student in the Disordered Systems group, has been awarded a Bronze medal at STEM for Britain in recognition of the excellence of her research on modelling the emergence of collective memory in societies.
Statistical Mechanics of Disordered Systems, Statistical Topology of Random Landscapes and Fields, Extremes of Random Processes, Anderson Localization, Quantum Chaotic Scattering
Low Temperature Properties of Glasses, Phase Transitions in Disordered Systems, Neural Networks, Risk Modeling, Random Matrices, Networks
Integrable quantum field theory, Conformal field theory, Entanglement entropy and out-of-equilibrium quantum systems
Non-equilibrium statistical mechanics, Soft matter, Systems biology, Bayesian inference, Random Matrices, Econophysics
Econophysics, Application of methods from Statistical Physics to Finance, Data Analytics, Complex Systems, Science of Networks
Random matrix theory, Applications of statistical physics to socio-economical sciences
Theory of spin glasses, Out of equilibrium dynamics, Real world networks, Graph dynamics, Stochastic processes
Non-equilibrium thermodynamics, Sparse non-Hermitian random matrices, Sequential hypothesis testing, Dynamics of receptors on membranes, Transport processes through networks, Dynamics of spin models on graphs, Neural networks
Random combinatorial problems, Inference, Assignment and transportation problems
Entanglement measures in many-body systems, QFT methods, Disordered many-body systems
Extreme value statistics, Rare events, Large deviations, RMT, Coulomb gas, Random landscapes, Random walks, Brownian motion, Branching processes, Active processes, Fluctuations in non-equilibrium systems
Quantum chromodynamics and Lattice gauge theory, Statistical Mechanics of Disordered Systems, Quantum Chaos and Scattering, Random Landscapes and Fields, Anderson Localisation
Working with Izaak Neri and Pierpaolo Vivo
Working with Alessia Annibale
Working with Benjamin Doyon and Paola Ruggiero
Working with Alessia Annibale and Reimer Kühn
Working with Izaak Neri
Working with Pierpaolo Vivo
Working with Yan Fyodorov and Pierpaolo Vivo
Working with Yan Fyodorov
Working with Yan Fyodorov
Working with Gabriele Sicuro and Pierpaolo Vivo
Working with Pierpaolo Vivo and Alessia Annibale
Dr. Pierpaolo Vivo’s team aims at measuring and taming the complexity of the UK legal system advocating a new digital, network-based approach to the visualisation and quantitative analysis of legal provisions.
The research activities of the group concentrate on the analysis and development of mathematical theories and models with which to describe the statics and dynamics of disordered (or “complex”) systems in physics, biology, financial markets, and computer science.
In the domain of physical systems, the question of how to pack spheres optimally is familiar from everyday examples such as a greengrocer’s stack of oranges. But what if the spheres have a range of sizes, as happens for example in colloidal suspensions?
The definition and generation of good null models to assess the statistical relevance of observed features in protein interaction networks (PIN) is a well known problem in systems biology, where the aim is to understand how the structure of PINs relates to their biological functionality.
A collaboration between group members prof. Reimer Kuehn and Dr. Perez Castillo and international collaborators also led to a breakthrough in the spectral problem for sparse symmetric random matrices, allowing to efficiently compute spectral densities of such systems in the limit of large matrix size to any desired accuracy – more than 20 years after a solution to this problem was first attempted.
Prof. Reimer Kühn has provided the first formulation of a microscopic model to describe the emergence of the universal glassy low-temperature anomalies, including an understanding of the origin of the mysterious so-called quantitative universality – a problem that had been open since its formulation in the late 80s.
A collection of minicourses given by members of the group on our fundamental research topics
Benjamin Doyon covers the fundamentals of Generalized Hydrodynamics in a mini-course at ICTS, Bangalore.
Yan Fyodorov discuss the number and stability properties of equilibria in large complex systems in a series of lectures given at the Park City Mathematics Institute.
Seminars given by members of the group on their research in institutions and events around the world.
Our meetings in which we discuss our research, look at new results, and invite guest speakers.