**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

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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.

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.

**Pierpaolo Vivo** gives brief course on random matrix theory given at ICTP Trieste, from the theoretical foundations to applications to complex systems.

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.

The seminar page of the Statistics group at King’s College.