Department of Mathematics

Prof Bryan P Rynne

I am an emeritus professor in the Mathematics Department of Heriot-Watt University. I joined the department in 1990, and became a reader in 1996, and then a professor in 2009. I retired in April 2021. Before that I was an RA on several contracts in a random sequence of British Universities. Between 2008-2012 I was the Chair of the Editorial Board of the Proceedings (Section A) of The Royal Society of Edinburgh. Between 2012-2015 I had the misfortune to be Head of Department in the Heriot-Watt Department of Mathematics. Following that I was promoted back to being a research mathematician.

Interests other than maths.

• Walking up mountains (UK and Europe mainly).

  In 2016 I finished doing all the 6 lists of mountains in the UK that the SMC (Scottish Mountaineering Club) maintains (viz., Munros + tops, 'furths', Corbetts, Donalds and Grahams - (see SMC Hill Lists).
  I also did the deleted Munros, on the grounds that if they were good enough for Munro then they are good enough for me.
  There are roughly 1000 of these (although I haven't counted them precisely).

  Outwith the UK I regularly go walking in Alpine countries.
  In 2019 (just before Covid) I did the well-known long-distance walk 'The Tour du Mont Blanc', and in 2022 (just after Covid) I did the GR20 in Corsica.

• Rock climbing - some photos.

  In summer, on the occasions when the sun shines, I go and dangle from ropes on vertical rock faces wishing I had real muscles rather than the mathematician's variety.
  This is a mix of climbing in the UK, and sports climbing in sunnier areas of the world, such as France, Spain, the US.

• Long-distance cycle touring.

  At one time or other I have probably cycled most of the nice roads in Scotland north of the central belt (there are not all that many of these!). Other times I go on long distance cycle tours in countries which are hot and dry, and produce lots of high-quality wine (so not Scotland), such as France, Spain, Italy, Austria, New Zealand.

Research interests

• Multiparameter (linear) spectral theory.
• Time domain electromagnetic scattering.
• Inverse scattering theory.
• Diophantine approximation theory.
• Multiparameter local bifurcation theory.
• Global bifurcation theory.
• Generic properties of solutions of nonlinear equations.
• Semi-linear boundary value problems with jumping nonlinearities.
• Multi-point boundary value problems.
• p-Laplacian boundary value problems: bifurcation theory for these, and also stability of equilibrium solutions.

Publications

Book

Linear Functional Analysis (with M A Youngson).