Mathematical models of opinion dynamics emerged in the mid-20th century, and seek to simulate the formation of consensus and disagreement in social groups. A phenomenon that has enjoyed particular attention over the past decades is the rise of a stable opinion plurality, or how multiple opinions can co-exist within a society for an extended period of time, possibly even indefinitely. Since the advent of social media, this focus has in places narrowed to the study of ‘polarisation’ as well as to the study of ‘opinion bubbles’: closed communities that have coagulated around a single opinion, and are unaware of or impervious to outside influence. Today, researchers have a plethora of tools at their disposal, ranging from mean-field methods over sophisticated data science to neural graph representation techniques, to understand and quantify the spread of information and the dynamics of opinions in social networks.

The aim of this talk is twofold: on the one hand, I will present and discuss some of the results of my Master’s thesis on social opinion dynamics, in which I extended the classical Deffuant model to include group dynamics and status homophily. Centrally, my model explains opinion polarisation not only as a consequence of opinion exchange, but also of social group dynamics. On the other hand, I wish to give a broader perspective on the field. How can mathematical and physical tools and insights contribute to understanding social opinion dynamics? What is the state of the field, what are its challenges, which lines of research appear most fruitful? And: what can we ultimately hope to gain from these models?