Martin Crane's current areas of research are biocomputation and econophysics. In the area of biocomputation, Dr. Crane is interested in the use of mathematics and computing to simulate drug dissolution and pharmacokinetics in vitro. He also explores applications of parallel computing to biosciences problems e.g. use of digital video as input data for Monte Carlo models of dissolution.

In the area of econophysics, Dr. Crane's work is focused on eigenanalysis of the financial covariance and correlation matrices for volatility/risk assessment. He also has a strong interest in agent-based models and co-operative behaviour in financial markets. Dr. Crane's research is in the general areas of mathematical modelling and (parallel) scientific computing. In the past, he has worked in such areas as finite elements for computational solid and fluid mechanics.

Dr. Crane's principal current source of funding is the Biocomputation Programme of the National Institute for Cellular Biotechnology (NICB), funded by HEA/PRTLI.