Advanced math for improved information processing
Representation of systems using random matrices has application not only to theoretical mathematics and physics, but also in areas including superconductor technology, signal processing and wireless communications, improving web search engines and even finance. Integral to the above applied fields are data storage and processing. Computers have revolutionised the speed with which numerical calculations can be made and led to solutions of more and more complex problems, both as a result of the increasing speed at which calculations can be performed and thanks to expanded computer memory for storing intermediate results. However, the speed and accuracy of computer computations depends not only on hardware but on numerical methods and, in particular, numerical stability. In the case of iterative methods such as those employed to solve many problems, speed and accuracy also depend on the convergence rate, or the rate at which the computer (via its mathematical software) hones in on the correct answer. Thus, improved numerical methods are of paramount importance. Applications of random matrix theory (RMT) to asymptotic problems for orthogonal polynomials and entanglement entropy in quantum spin chains is the focus of ‘The Riemann-Hilbert problem and random matrix theory’ (RHP-RMT) project. The project team also has the goal of training a research Fellow in new areas related to his previous research. To date, the Fellow has made significant progress regarding orthogonal polynomials, with a corresponding manuscript in preparation. In addition, he has recently started working on entanglement entropy in collaboration with colleagues and has attended two special seminars in the United States. The results of the RHP-RMT project will not only advance the fields of theoretical mathematics and physics, but could have an impact on fields as diverse as quantum communications and finance.
