## Backward differential equations

This board was created in the common room of the School of Mathematics at the University of Edinburgh by David Siska and Arnaud Lionnet. Arnaud is visiting David in Edinburgh, and they are working on backward stochastic differential equations and stochastic partial differential equations, which are on the interface between probability and analysis.

## Blackboard cake

This birthday cake was made for Robin Knops, a Professor Emeritus at Heriot-Watt University, to celebrate his 80th birthday. The celebrations were part of a conference at ICMS in Robin’s honour, which was especially fitting as Robin was one of the founders of ICMS (the International Centre for Mathematical Sciences) in 1990. This cake was ordered from a Fife company called Sucre Coeur, with the mathematical equation suggested by Penny Davies.

The first equation is just a representation of the fact that the sum of Robin’s years is 80.

The second equation is the equation of conservation of linear momentum: rho = density, v = velocity, T = stress tensor, b = body force (e.g. something like gravity). Penny says “The version on the cake refers to using an Eulerian (deformed) coordinate system, and this is more usual for fluids than for solid mechanics (which Robin has worked far more on and uses the reference or Lagrangian coordinate system). This would normally have a suffix “R” on the rho and T terms, and so wouldn’t have been so easy to typeset on a cake.”

We wish Robin many happy returns (although his actual birthday is not until 30th December).

## Sobolev spaces

This photo was taken in the former office of Sandy Davie, a recently retired professor at the University of Edinburgh. The writing on the board is the result of conversations with another professor, Istvan Gyongy, about partial differential equations in Sobolev spaces. It’s a great example of a typical mathematician’s blackboard, with chalk being drawn over old chalk and some evidence of half-hearted rubbing out with hands. Mathematicians usually prefer to make this kind of a ‘mess’ rather than interrupt the flow of ideas to clean the board properly.