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.
Education
The Cross-Disciplinary Approaches to Non-Equilibrium Systems Centre
CANES is an EPSRC Centre for Doctoral Training with an active participation of the DS Group.
MSc Complex System Modelling
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.
Apply to the KCL MPhil/PhD Mathematics Program
KCL Mathematics department produces excellent or world-leading research in terms of originality, significance and rigour. Join KCL for your postgraduate studies!
News
Latest from the group on X
Disordered Systems Days at King’s College London
A two-day workshop to celebrate Reimer Kühn.
Spin Glass Theory & Far Beyond
An encyclopaedic overview of the broad range of the applications stemming from the discovery of the replica symmetry breaking solution of the Sherrington-Kirkpatrick model by Giorgio Parisi. Gabriele Sicuro participated to the editing of this publication, which includes a contribution by Yan Fyodorov.
The Facets of Statistical Field Theory
A conference on Statistical Field Theory, Statistical Physics and their interdisciplinary applications in Trieste, in honour of Sergio Caracciolo’s 70th birthday, organise, amongst the others, by Gabriele Sicuro.
Random Matrices and Random Landscapes
A conference in Ascona on the mathematics of complex physical systems, with an emphasis on the interaction between mathematics and physics, to celebrate the 60th birthday of Yan Fyodorov.
MECO47
The traditional Conference of the Middle European Cooperation in Statistical Physics is organised this year by Silvia Bartolucci, Laura Foini, Gabriele Sicuro and Pierpaolo Vivo in Erice.
73rd British Mathematical Colloquium
The British Mathematical Colloquium will be hosted at King’s College London, and will include a special session on complex systems with a list of prestigious guests including Andrea Montanari and Vittoria Colizza.
Welcoming the 2021 Nobel Prize for Physics to Giorgio Parisi
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.
Random Matrix Theory and Networks Workshop
Izaak Neri is scientific coordinator of the virtual workshop organized at MPI, that aims to bring together researchers working on random matrix theory and complex systems.
Events
Events, conferences and workshops organised by the group
Disordered Systems Days at King’s College London
A two-day workshop to celebrate Reimer Kühn.
Spin Glass Theory & Far Beyond
An encyclopaedic overview of the broad range of the applications stemming from the discovery of the replica symmetry breaking solution of the Sherrington-Kirkpatrick model by Giorgio Parisi. Gabriele Sicuro participated to the editing of this publication, which includes a contribution by Yan Fyodorov.
The Facets of Statistical Field Theory
A conference on Statistical Field Theory, Statistical Physics and their interdisciplinary applications in Trieste, in honour of Sergio Caracciolo’s 70th birthday, organise, amongst the others, by Gabriele Sicuro.
Random Matrices and Random Landscapes
A conference in Ascona on the mathematics of complex physical systems, with an emphasis on the interaction between mathematics and physics, to celebrate the 60th birthday of Yan Fyodorov.
MECO47
The traditional Conference of the Middle European Cooperation in Statistical Physics is organised this year by Silvia Bartolucci, Laura Foini, Gabriele Sicuro and Pierpaolo Vivo in Erice.
73rd British Mathematical Colloquium
The British Mathematical Colloquium will be hosted at King’s College London, and will include a special session on complex systems with a list of prestigious guests including Andrea Montanari and Vittoria Colizza.
Welcoming the 2021 Nobel Prize for Physics to Giorgio Parisi
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.
Random Matrix Theory and Networks Workshop
Izaak Neri is scientific coordinator of the virtual workshop organized at MPI, that aims to bring together researchers working on random matrix theory and complex systems.
Meet the group
Faculty
Yan Fyodorov
Chair in Disordered Systems
Statistical Mechanics of Disordered Systems, Statistical Topology of Random Landscapes and Fields, Extremes of Random Processes, Anderson Localization, Quantum Chaotic Scattering
Benjamin Doyon
Professor of Theoretical Physics
Integrable quantum field theory, Conformal field theory, Entanglement entropy and out-of-equilibrium quantum systems
Leonid A. Pastur
Professor of Probability
Random Matrices, Spectral theory of random Schrödinger operators
Ivan Tyukin
Professor of Mathematical Data Science and Modelling
Industrial Mathematics, Dynamical Systems, Adaptive Control, Neural Networks, Certified Artificial Intelligence
TBA
Professor
Tiziana di Matteo
Professor of Econophysics
Econophysics, Application of methods from Statistical Physics to Finance, Data Analytics, Complex Systems, Science of Networks
Pierpaolo Vivo
Reader in Disordered Systems
Random matrix theory, Applications of statistical physics to socio-economical sciences
François Huveneers
Reader in Disordered Systems
Probability theory, Mathematical physics, Out-of-equilibrium statistical mechanics
Izaak Neri
Senior Lecturer in Disordered Systems
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
Alessia Annibale
Senior Lecturer in Disordered Systems
Theory of spin glasses, Out of equilibrium dynamics, Real world networks, Graph dynamics, Stochastic processes
Matteo Tanzi
Lecturer in Disordered Systems and Analysis
Dynamical Systems, Ergodic theory
Paola Ruggiero
Lecturer in Disordered Systems
Entanglement measures in many-body systems, QFT methods, Disordered many-body systems
Rosalba García-Millán
Lecturer in Disordered Systems
Postdoctoral researchers
Thibault Bonnemain
Postdoctoral researcher
Integrability and many body systems, Hydrodynamics, Soliton gases, Mean field games
Tim Würfel
Postdoctoral researcher
Quantum chromodynamics and Lattice gauge theory, Statistical Mechanics of Disordered Systems, Quantum Chaos and Scattering, Random Landscapes and Fields, Anderson Localisation
Bertrand Lacroix-A-Chez-Toine
Postdoctoral researcher
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
Evangelos Tzanis
Postdoctoral researcher
Jan Meibohm
Humboldt Visiting Research Fellow
Non-equilibrium statistical mechanics, Fluid mechanics, Non-linear dynamics
PhD Students
Adarsh Raghu
PhD Student
Working with Izaak Neri
Friedrich Hübner
PhD Student
Working with Benjamin Doyon and Paola Ruggiero
Gyeong-Gyun Ha
PhD Student
Working with Izaak Neri and Alessia Annibale
Luca Gamberi
PhD Student
Working with Pierpaolo Vivo
Mark Crumpton
PhD Student
Working with Yan Fyodorov and Pierpaolo Vivo
Mohammed Osman
PhD Student
Working with Yan Fyodorov
Preben Forer
PhD Student
Working with Pierpaolo Vivo
Urtė Adomaitytė
PhD Student
Working with Gabriele Sicuro and Pierpaolo Vivo
Projects
Quantitative and Digital Law Lab
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.
Disordered systems
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.
Physical Systems
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?
Protein interaction network
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.
Sparse Symmetric Random Matrices
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.
Universal Glassy Low-Temperature Anomalies
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.
Advanced courses
A collection of courses given by members of the group on our fundamental research topics.
Generative AI and Diffusion Models: a Statistical Physics Analysis
A course by Giulio Biroli from École Normale Supérieure de Paris.
Generalised Hydrodynamics
A course by Thibault Bonnemain on the theory of generalised Hydrodynamics.
Quantum Entanglement in Disordered Systems
A course by Leonid Pastur on the effects of disorder on quantum correlations and entanglement.
Conformal field theory and quantum many-body physics
Benjamin Doyon on CFT and quantum many-body physics at CRM, leading research institute in mathematics in Canada.
Least-square optimization on the sphere: lessons from RMT and replicas
Pierpaolo Vivo gives brief course on applications of random matrix theory to optimisation problems.
Generalized hydrodynamics
Benjamin Doyon covers the fundamentals of Generalized Hydrodynamics in a mini-course at ICTS, Bangalore.
Counting equilibria in complex systems via random matrices
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.
Random matrices: Theory and Practice
Pierpaolo Vivo gives brief course on random matrix theory given at ICTP Trieste, from the theoretical foundations to applications to complex systems.
Talks and Colloquia
The Group Research
Seminars given by members of the group on their research in institutions and events around the world.
The King’s Mathematical Colloquia
A series of Colloquia given by word-leading experts in Mathematics at King’s College London.
The Disordered Systems Group Journal Club
Our meetings in which we discuss our research, look at new results, and invite guest speakers.
The Statistics seminar series
The seminar page of the Statistics group at King’s College.