The Maxwell Institute encompasses all areas of modern mathematical sciences research ranging from pure subjects to applications. On the pure side, there is work in traditional core areas such as algebra, analysis, geometry, and topology.
Our work also encompasses fluid dynamics, computational mathematics, and applied dynamical systems, with applications to specific topics in biology, chemistry, engineering, geosciences, informatics, physics. A key theme arising frequently in modern applications is the need to model uncertainty, a topic addressed in various directions in our research in probability and statistics. Another area of work is operational research, which deals with the application of advanced mathematical methods to help make better decisions for business and social policy.
Research work in the Maxwell Institute has been funded by dozens of awards (worth millions of pounds) from the UK's Engineering and Physical Sciences Research Council and the Scottish Funding Council.
Some specific grants have included:
- An EPSRC Science and Innovation grant in 2007 creating the Centre for Analysis and Nonlinear Partial Differential Equations (CANPDE) which addresses a wide range of problems related to the fundamental properties of this very important class of equations.
- An EPSRC/SFC Science and Innovation award in 2009, establishing the Centre for Numerical Algorithms and Intelligent Software (NAIS), expanding our activities in computational mathematics and operational research and by establishing vital links with computer scientists, high performance computing researchers, and industrial users.
- SFC support for the foundation in 2010 of the Scottish Financial Risk Academy (SFRA) which provides a conduit for our research in financial and actuarial mathematics to impact on the financial industry.
- A grant form the Science and Technology Facilities Council to found the Tait Institute, a focal point for research in mathematical physics across Edinburgh.
Our achievements in interdisciplinary research are evidenced by the above grants and by an EPSRC Bridging the Gaps award, in a substantial EPSRC grant on adapting building design to climate change, and in a major collaborative EPSRC project on mathematical foundations of energy networks. An industrial award from the financial sector for PhD scholarships and the establishment of the Actuarial Research Centre exemplify the diversification of our funding sources. Our investment in the The International Centre for Mathematical Sciences (ICMS) has been rewarded by a considerable expansion of the centre's activities with funding provided by major EPSRC and SFC grants.