The Department of Mathematics, which has more than doubled in size in recent years, now comprises three major research groups. The defining focus of each is intended to influence as well as benefit from the LSE’s unique emphasis on social sciences. Indeed, the Department’s development has largely been driven by its intentions to strengthen synergies with other leading LSE groups in related disciplines such as economics, finance, management and statistics.
Research in discrete mathematics and algorithms spans topics ranging from those in pure mathematics, such as extremal and structural properties of (hyper)graphs, probabilistic methods and combinatorial geometry, to more applicable topics, such as machine learning and algorithmic aspects of massive data sets. The group also has close ties with the operations research group in the LSE Department of Management.
The financial mathematics and control theory group, together with the risk and stochastics group in the LSE Department of Statistics, forms one of the world’s biggest concentrations of researchers in this area. Its research is mostly concerned with pricing, hedging and equilibria in markets with frictions and asymmetric information structures, the study of alternative markets such as energy markets and methodological approaches to stochastic control and optimal stopping.
The game theory group presents one of the world’s highest concentrations of game theorists within a mathematics department. It explores several aspects of mathematical game theory, with special interests in areas including the strategic use of information, stochastic games, and algorithmic game theory.
The Department’s ambition to produce world-class mathematical research is coupled with a commitment to consider ‘real-world’ challenges. Amol Sasane’s research in mathematical control theory provides a prime example, supporting Boeing’s patented design of flight control systems intended to optimise the aerodynamic performance of aircraft, resulting in improvements in both fuel efficiency and flight safety.
The Department shares research results beyond academia via contributions to professional and practitioner events, including workshops organised by Telefonica and Microsoft. Engagement with private sectors such as finance, consultancy, logistics and IT is facilitated by the fact that many of the Department’s graduates (BSc, MSc, as well as PhD) find work within those sectors.
The Department also takes a proactive approach to stimulating public interest in mathematics, sometimes using innovative external opportunities: in 2013 a graphical representation of a mathematical model of racial segregation, produced by Andy Lewis-Pye and colleagues, took first place in the Infographics’ category of the Royal Society’s Picturing Science competition .