We will discuss nonlinear cross-diffusion models describing cell motility of two distinct populations. The continuum PDE model is derived systematically from a stochastic discrete model consisting of impenetrable diffusing spheres. In this talk, I will outline the derivation of the cross-diffusion model, discuss some of its features such as the gradient-flow structure, and show numerical results comparing the discrete stochastic system to the derived model.

Euler’s equation, the ‘most beautiful equation in mathematics’, startlingly connects the five most important constants in the subject: 1, 0, π, e and i. Central to both mathematics and physics, it has also featured in a criminal court case and on a postage stamp, and has appeared twice in The Simpsons. So what is this equation – and why is it pioneering?

Robin Wilson is an Emeritus Professor of Pure Mathematics at the Open University, Emeritus Professor of Geometry at Gresham College, London, and a former Fellow of Keble College, Oxford.

28 February 2018, 5pm-6pm, Mathematical Institute, Oxford

Please email @email to register

Bacteria swim by rotating semi-rigid helical flagellar filaments, using an ion driven rotary motor embedded in the membrane. Bacteria are too small to sense a spatial gradient and therefore sense changes in time, and use the signals to bias their direction changing pattern to bias overall swimming towards a favourable environment. I will discuss how interdisciplinary research has helped us understand both the mechanism of motor function and its control by chemosensory signals.

Please see https://www.eventbrite.co.uk/e/qbiox-colloquium-dunn-school-seminar-hil…

for details.

We describe a locally finite graph naturally associated to each knot type K, called the Reidemeister graph. We determine several local and global properties of this graph and prove that the graph-isomorphism type is a complete knot invariant up to mirroring. Lastly (time permitting), we introduce another object, relating the Reidemeister and Gordian graphs, and briefly present an application to the study of DNA.