The Corcoran Memorial Lecture and Memorial Prize is a biennial event.  The prize is awarded to students of the Department of Statistics for outstanding graduate work. We are delighted to announce that the winner of the 2018 Corcoran Memorial Prize is Dr Sarah Penington. The prize will be awarded at the Corcoran Memorial Prize Award and Lecture on Friday 31st January 2020.

Speaker: Professor Frank den Hollander, Leiden University

Title: Synchronisation with noise

Abstract: Spontaneous synchronisation is ubiquitous in nature. Single oscillators (like flashing fireflies, chirping crickets or spiking brain cells) may rotate incoherently, at their own natural frequency, when they are isolated from each other. But within a population they adapt their rhythm to that of the other oscillators, acting as a system of coupled oscillators. There is no global driving mechanism, yet the population reaches a globally synchronised state via mutual local interactions.

In this lecture we focus on the Kuramoto model, a mathematical model that describes interacting phase oscillators on a network. Each node of the network carries an oscillator that is subject to noise. Pairs of oscillators interact with each other along the bonds of the network, at a given interaction strength. In the limit as the size of the network tends to infinity, there is a phase transition between an unsynchronised state and a synchronised state as the interaction strength crosses a critical threshold.

What makes the Kuramoto model exciting and challenging is that the interaction between the oscillators is non-linear. This allows for a very rich behaviour as a function of the underlying network. We focus on networks with a community structure. The biological clock of humans is located in the brain, in the so-called suprachiasmatic nucleus, which consists of two networks of neurons that are linked together. We will describe some of the features of the biological clock and relate them to the Kuramoto model.

List of Corcoran Memorial Lectures.