Theory of human enterprise
Developing mathematical models of markets, innovation and organisations, so that we can predict them and enhance them through interventions.
Science has traditionally been concerned with the natural world. But as society gets more interconnected and organisations get bigger, the man-made world needs a science of its own.
The sentiment of borrowers and lenders in a financial network is what drives markets to success, but also to ruin. We develop mathematical methods to predict how distress spreads, and determine strategies to limit system-wide catastrophic failure. We determine the latent potential in countries and firms by applying spectral-like theories to their networks of products and capabilities.
Despite advances in our understanding of evolution, what drives innovation remains elusive. Technological innovation operates in an expanding space of building blocks, in which combinations of technologies become new technologies. We characterise innovation in a mathematical way, extracting concepts and conservation laws, so that we can predict and influence it.
Organisations have emergent properties and capabilities that we are just coming to terms with. The success of some wikis suggests that many non-interacting agents can produce creative works superior to what any one person could do alone. What is the mathematical basis for collective creativity, and what sectors can we apply it to? Can it be used to speed up discovery in physics and mathematics?
Creating a mathematical model of combinatorial innovation to understand how innovation rates can be influenced as components are acquired.
Using ideas from statistical physics to reconstruct the average properties of financial networks from partial sets of information.