## 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.

## Deformation theory and 3-folds

This photo is of the blackboard in the common room of the School of Mathematics at the University of Edinburgh. The workings on the left are by Michael Wemyss, drawn while he was talking about deformation theory (a generalization of differential calculus) with Will Donovan, as part of their work on the geometry of certain spaces, known as 3-folds. Will says, “Deformation theory lets us express the way in which a curve in a 3-fold can `move’ infinitesimally: we can then relate this to the (quantum) geometry of the 3-fold. I’ve tried to emulate Michael’s calligraphic F’s and G’s, but I haven’t had any success yet.” We don’t know who did the workings on the right.

## Fourier Piggy

I got sent this photo from Piggy who has a blog about exciting things he finds in science and maths. There are actually lots of fun whiteboards amongst his blog posts; for example this one about using mathematical analysis to design a strategy for hitting on the opposite sex.

In this photo, Piggy had to help a friend and explain to him the Fourier series representation of periodic and non periodic functions. He started easy, saying that Fourier had this great idea of resolving the problem in its various frequencies and then summing everything up. But then he got excited and dropped integrals here and there.

## A course in real analysis

This photo is from Marko Budisic at the University of California in Santa Barbara. He says that it was taken a while back, in 2007, when he was taking Chuck Akemann‘s graduate course in real analysis at UC Santa Barbara. Marko thinks that the writing on the left might be one of the homeworks, but I also love all the random scribblings on the right.

## 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 chalkĀ 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.