Cascade dynamics can occur when the state of a node is affected by the states of its neighbours in the network, for example when a Twitter user is inspired to retweet a message that she received from a user she follows, with one event (the retweet) potentially causing further events (retweets by followers of followers) in a chain reaction. In this talk I will review some mathematical models that can help us understand how social contagion (the spread of cultural fads and the viral diffusion of information) may depend upon the structure of the social network and on the dynamics of human behaviour. A particular focus will be on an analytically tractable model for meme propagation, and a time-dependent metric that accurately captures the change in the relative influence of nodes over the duration of a cascade.
Professor James Gleeson holds a BSc in Mathematical Science and an MSc in Mathematical Physics from University College Dublin. In 1999 he completed his Ph.D. in Applied Mathematics at Caltech. He has lectured at Arizona State University and at University College Cork, and since 2007 has held a Chair in Industrial and Applied Mathematics at the University of Limerick. James’ research interests are in the mathematical modelling of stochastic dynamics, with a particular focus on complex systems and networks. James is Head of the Department of Mathematics and Statistics at UL, is an associate editor of the Journal of Complex Networks, and has served as a member of the editorial board of Physical Review E and of the Scientific Advisory Board of ISI Foundation Turin. He is a Director of the Research Ireland Centre for Research Training in Foundations of Data Science and a PI of the Insight Research Ireland Centre for Data Analytics. He served as a member of the Irish Epidemiological Modelling Advisory Group (IEMAG) that provided mathematical and statistical modelling advice to Ireland’s National Public Health Emergency Team (NPHET) during the COVID-19 pandemic.
