MSI Weekly Bulletin - Week starting Monday 27 March, 2006

Background: Applications of mathematics and statistics, and in particular mathematical modelling, play a central role in an increasing range of fields. These areas are critical to the future, through the enabling role they play in science and engineering, health, social science and public policy. This is illustrated by dramatic advances in communications technology, the understanding of risk, and methods for dealing with large complex datasets, e.g. bioinformatics. Often mathematical or statistical approaches developed in one scientific area can usefully be applied in other areas, yet it can be extremely difficult to find out who may be working on essentially similar problems when the application areas are diverse.To bring together researchers with interests and expertise in various AMS and provide networking opportunities and resources we will be holding a series of lunchtime colloquid (followed by lunch) and poster evenings (accompanied by drinks and nibbles), so that researchers, staff and students can learn from each other about mathematical and statistical approaches and tools that may be useful for problems in different areas.

There are many functions which interpolate the factorial function for non-integer arguments, such as the Gamma function. We will present a proof that the Gamma function is however the only such function which is also log-convex.

Optimal transportation concerns the minimization of cost functionals associated with measure preserving mappings. The subject began over 200 years ago with the famous Monge problem of moving soil with the least amount of work. In recent years there has been a massive rejuvenation of the area with tremendous advances in the theory, including the complete resolution of the original Monge problem, and a diverse range of applications. This lecture treats the relationship with classical elliptic PDE theory and the traditional calculus of variations. In particular we report on recent work of Loeper, Ma, Wang and the speaker on the characterization of costs for which smooth solutions are possible.