This is a growing list of talks I have given to non-expert audiences.
A hopefully simple lecture aimed at undergraduates about how string theory alters our geometrical intuition. (A little dated now: this was written as the second superstring revolution was unfolding.)
A colloquium-style talk for mathematics PG students about how to listen to the shape of the universe from the cosmic microwave background.
A light-hearted general-interest talk aimed at Edinburgh maths undergraduates, tracing the notion of space from Newton to the present day.
A talk about ADE classifications: from Platonic solids and their use by Kepler, to finite subgroups of unit quaternions and their recent appearance in the physics of M2 branes.
An introduction to the Higgs mechanism for UG mathematics students, first given in February 2013 during Edinburgh's Innovative Learning Week.
A talk in Spanish about the mathematics of Japan during the Edo period (wasan) and propagated via votive tablets (sangaku) hung in temples and shrines. A version in English shall appear here eventually.