### Latest

## Combinatorics of non-crossing partitions

## Board of pi

This board by David Cushing at Newcastle University attempts to calculate pi very crudely by counting how many squares a circle covers and using the formula

Area = pi x r^{2}

to get a value of 2.98. Can you do better?

This exercise was part of a series of activities carried out to celebrate “Ultimate pi day” on 3/14/15 (in US date format). There were also many other attempts by people to estimate the value of pi using nonstandard methods. Did you take part in the festivities and, if so, how?

## 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.

## Self-intersection numbers for a fence

This is the board of Chris Palmer, a postgraduate at the University of Edinburgh. He has recently been working on finding a simple chain level Seifert pairing for the Seifert surface of a link. This is related to his supervisor Andrew Ranicki’s recent talk in which he used surgery theory to find a chain level pairing. The figures show how to compute the self intersection numbers for a fence (a one-dimensional simplicial complex that is a deformation retraction of the Seifert surface).

## Backdrop for Sir Michael Atiyah

Today the University of Edinburgh was privileged to welcome award-winning photographer James Glossop to the School of Mathematics. His task was to photograph Sir Michael Atiyah for an article in The Times (to appear next week) and he asked for a blackboard to be decorated with mathematical equations to form the backdrop to this photo. It was a joint effort between Andrew Ranicki, Julia Collins, Patrick Orson, and (of course) Sir Michael, and contains all their favourite formulae, numbers and ideas in mathematics. What would *you* have drawn on the board?

James kindly took this photo of the board after he was finished getting his shots of Sir Michael. I like the heavenly light shining in from above!

## Niels Bohr Institute

This is the blackboard in the common room at the Niels Bohr Institute in Copenhagen, taken by Andrew Jackson. It is advertising a colloquium given by Julia Collins about Peter Guthrie Tait, with a helpful diagram of a vortex cannon to show people what to expect in the talk. Unrelatedly, there is a lot of matrix algebra on the left and what seems to be a half-rubbed-off torus on the right. Proof that even in a physics institute, much of the work is really mathematics! We have no idea what the cartoon at the top signifies.

## Inverse blackboard

Christian Perfect and David Cushing spent the morning computing inverses using their special inverse blackboard.

Going left-to-right and top-to-bottom, we have:

- The inverse of a 2×2 matrix;
- The commutative diagram for the universal property of the inverse limit;
- A variable which is inversely proportional to another;
- The inverse of a complex number;
- The derivative of the inverse of a function;
- The inverse tangent of 1;
- The axiom for group inverses;
- Part of the definition of the logical inverse.

Thanks Christian and David for this wonderful idea!

## Doors Open Day

On Saturday 28 September 2013 many interesting buildings in Edinburgh opened their doors to the public for Doors Open Day. One of these was ICMS – the International Centre for Mathematical Sciences – on South College Street. ICMS are in a building that used to be a church and still has a beautiful stained glass window, but now the only worshipping which goes on is for mathematics! Visitors were invited to solve puzzles and play mathematical games, and to draw their favourite maths on this blackboard. What would you have drawn?

## 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.

## Knot concordance and slice movies

This board belongs to University of Glasgow researcher Brendan Owens. The pictures on the right show a ‘slice movie’ which is used to prove that two knots are concordant to each other. The pictures are essentially 3D slices through a 4D disc; the ‘singularity’ where two parts of the knot appear to intersect is an illusion caused by the particular projection. The long exact sequences on the left are the technical algebraic topology used to explore the crazy world of 4-dimensional knot theory, where geometrical intuition so frequently fails.