Adtones intelligently tailors mobile ads to users in developing countries and shares the revenue with them to subsidize their phone bills.

Adtones

Boston Consulting Group is a management consulting firm that advises businesses and organizations on strategy, transformation and growth.

Boston  Consulting Group

The BCG Henderson Institute applies insights from academic disciplines to the strategic challenges facing business, government and society.

BCG Henderson Institute

Bit Bio is a human synthetic biology enterprise, which reprograms human cells for use in research, drug discovery and cell therapy.

BitBio

Cancer Research UK supports scientific and medical research to help beat cancer sooner. It is the world's largest cancer research charity.

Cancer Research UK

The Centre for Defence Enterprise funds research that could lead to a capability advantage for the armed forces and national security.

Centre for  Defence Enterprise

The U.S. Defence Advanced Research Projects Agency makes pivotal investments in breakthrough technologies that benefit national security.

Defence Advanced  Research Projects Agency

The U.S. Defence Threat Reduction Agency funds research to prepare for and combat weapons of mass destruction and improvised threats. 

Defence Threat  Reduction Agency

The European Innovation Council funds world-class scientists and innovators to develop and accelerate disruptive technology businesses.

European  Innovation Council

Framework Programme 7 was created by the European Commission to fund scientific research and innovation in Europe and associated countries.

Framework Programme 7

The Garfield Weston Foundation supports a range of charities across the UK and the restoration and redevelopment of their buildings.

Garfield Weston  Foundation

Horizon 2020 was created by the European Commission to fund scientific research and innovation across Europe and other member countries.

Horizon 2020

Invenia is a company of scientists and engineers that uses machine learning to optimize complex decision making and reduce inefficiencies.

Invenia Labs

LIMS Ventures is the start-up incubator of the London Institute which accelerates projects with potential for widespread commercialization.

LIMS Ventures

The Medical Research Council, one of the seven UK Research Councils, supports basic and applied medical research throughout the UK.

Medical Research Council

The U.S. Office of Naval Research supports basic research and technology for future naval power and the preservation of national security.

Office of  Naval Research

The Pilgrim Trust supports the preservation of architecturally important buildings and historically significant artifacts and documents.

Pilgrim Trust

The Porter Foundation supports projects in education, the environment, culture, health and welfare that encourage excellence and innovation.

Porter Foundation

The Rose Foundation provides financial assistance to charities undertaking building restoration and development in and around London.

Rose Foundation

The Edward Harvist Trust supports organisations that improve the quality of life for local people in Westminster and other London boroughs.

Edward Harvist Trust

The European Commission Migration and Home Affairs supports research to ensure the security of the EU and cooperation with non-EU countries.

European Commission  Migration and Home Affairs

The London Institute for Mathematical Sciences

Consistent valuation of interbank claims within an interconnected financial system can be found with a recursive update of banks' equities.

Finance network valuation

We’re hiring Postdoctoral Research Fellows in the theory of cell programming from the fields of physics, mathematics or machine learning.

We’re hiring postdocs

Britain is perfectly placed to replicate the DARPA miracle, but it will need to embody the qualities that have made the agency exceptional.

Viral DARPA

The ability of deep neural networks to generalize can be unraveled using path integral methods to compute their typical Boolean functions.

Deep layered machines

Statistical methods that normally fail for very high-dimensional data can be rescued via mathematical tools from statistical physics.

A fix for overfitting

Capturing in simulations and mathematical form the surface structure of crystals and how they coalesce when heated but not melted.

At the surface of crystals

Developing new local and global measures for networks derived from social interactions to infer social structure, sentiment and behaviour.

Extracting meaning from social networks

Bootstrap percolation originated as a simple cellular automata model of the spread of infection. Given a set of initially infected sites, in consecutive rounds sites become infected if they satisfy a certain infection rule, for example, more than a given number of their neighbours are infected. Percolation occurs if every node is eventually infected.
In this project we investigate the typical and extremal properties of bootstrap percolation for various infection rules and underlying networks. For sites that are initially randomly infected, we study the critical density of infection that leads to percolation. Alternatively, if the initial infected sites are set by hand, we study how many infected nodes are necessary to infect the whole network.
Bootstrap percolation can be used to model many real-life phenomena, such as pandemics, computer network failure, ferromagnetic behaviour, the spread of voting preferences and information processing in neural networks. A better mathematical theory will help us understand these processes and draw reliable conclusions well beyond what can be achieved through computer simulations.

Advancing the mathematical theory of bootstrap percolation, where active cells on a lattice with few active neighbours cease to be active.

Leaps in long-range connectivity

Is space a continuum or is it composed of a discrete set of points? Once a purely philosophical question, there is now a pressing need to describe space and space-time as discretized in order to resolve quantum gravity. Yet despite sophisticated attempts at discretizing space, researchers have failed to construct even the simplest geometries.
In this project we investigate models of discrete space in which continuum-like behavior is recovered at large lengths. We show that if space is discrete, it must be disordered, and develop explicit recipes for growing disordered discrete space by sampling distributions of graphs at low temperature. We also pursue graph formulations of non-Euclidean metrics, especially the Minkowski metric from special relativity.
Models of discrete space and space-time could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of the real numbers, which has no direct observational support. They also set the stage for digital physics, in which information takes centre stage in describing the universe.

Creating discrete models of space and spacetime that appear continuous over long lengths and set the stage for non-continuum physics. 

Is continuous space an illusion?

Densely packed objects of a similar shape, from rocks to foams to spheres, have intrigued mathematicians since the ancients. The mechanical properties of these materials are determined by how big the gaps are between them—in particular, how close they are to their maximum random-packed density. Predicting this maximum, and how the material properties vary around it, is a geometric and physics challenge.
In this project we investigate the packing of spheres of the same size and mixtures of spheres with a range of sizes. While simulating packing is easy to program, the running time scales poorly with system size. To overcome this obstacle, we develop new mathematical techniques for determining the properties of dense packings using a simplified 1d model. This powerful approach captures essential features of higher-dimensional systems.
Understanding how objects fit closely together under pressure or by design is at the heart of materials science and branches of fluid dynamics. Predicting the behaviour of dense packings also sets the stage for reverse-engineering new composite materials to have desired properties.

Predicting the geometry and behaviour of densely packed objects in the natural and man-made worlds, from rocks to foams to spheres.

At the surface of crystals

The London Institute for Mathematical Sciences gives scientists the freedom and support to make fundamental discoveries.

Papers

Finance network valuation

News

We’re hiring postdocs

Perspective

Viral DARPA

Papers

Deep layered machines

Where we publish

Who's funding us