There are myriad career paths open to PhDs in mathematical analysis - from academic research to industry and beyond. With this in mind, the Cambridge Centre for Analysis has fostered close ties with industry.
Analysis in industry
Here are just a few examples of how mathematical analysis is used in industry:
Oil reservoir design: This mostly involves fluid mechanics, computational analysis and some stochastic analysis. Examples of major companies in this field, that we are in close contact with, are Schlumberger Research or BP Research.
The design of transport networks involves stochastic analysis, operation research and, increasingly, nonlinear PDEs.
The design of modern aeronengines involves a combination of computational analysis (with computational solution of the Navier Stokes equations for industrial geometry proving particularly demanding), physical insight, modelling and experimental testing. One of the two main producers of modern aero engines is Rolls Royce, with whom we are in contact.
Onto something completely different: data mining and, with greater generality, making sense of huge amounts of data. This subject didn't really exist 30 years ago, but now all you need to think of is the importance of Google or the Human Genome Project to see how important an area this is. Both are dealing with very different types of data, but the maths is quite similar: stochastic, computational and harmonic analysis, coupled with a large measure of numerical algebra and even some abstract algebra. Our connection within this field is the Sanger Institute.
From data mining to image processing, which is now a huge industry, from NASA all the way to Pixar, using techniques from all over analysis: PDEs, computation, stochastics, harmonic analysis, even geometry of Banach spaces. In this area, we have excellent lines of communication with Microsoft Research Cambridge.
And from image to signal processing: here, again, analysis comes to the fore in the modern approach to the subject which includes radar imaging, information transmissions and recovery and much more. Indeed, this is one of the areas where mathematics in its generality has been having a huge impact in the last few years.
Did we mention weather forecasting? Stochastic analysis, fluid dynamics, computational analysis are all involved. The Met Office is a huge player and we are in close communication with them.
Analysis in academe
Some examples of current thesis topics being researched by CCA students:
- Stability and hypocoercivity issues in gas dynamics (under Dr Clément Mouhot)
- Black hole stability problem (under Professor Mihalis Dafermos).
- Infinite fragmentation processes (under Dr Nathanael Berestycki)
- Wiener-Hopf factorisation and wave scattering (under Professor Nigel Peake).
- Geometric measure theory (under Dr Neshan Wickramasekera)
- Higher-order regularity in imaging (under Dr Carola Schoenlieb)