CIM Colloquium 2025

The CIM Colloquium is a Mathematical Sciences event taking place before the annual council of the CIM Associates. This year the lecture will be delivered by Susana Gomes (The University of Warwick), on April 2nd, at 2 pm (Lisbon time).

The mathematics of opinion dynamics on evolving networks

Abstract: The field of opinion dynamics has recently seen a large interest from the mathematics community, both from modelling and control perspectives. Most works focus on the Hegselmann-Krause model, a bounded confidence model that assumes everyone can communicate with everyone else as long as their opinions are close enough. Typical results focus on analysing whether the system achieves consensus, and control strategies aim to steer a population towards consensus (or make it so more quickly) by using controls that act directly on agents. These models can be made more realistic if one introduces a social network that constrains communication between agents and if the controls are restricted.  

In this talk, I will introduce recent work on co-evolving networks (i.e. a dynamical system where the underlying network evolves at the same time as, and influenced by, the individuals' opinions), and justify why the resulting models can be obtained as a limit of one to one interactions in the right conditions. I will then propose a new type of control based on adaptive networks: I will present various control strategies and analyse under which conditions opinions can or cannot be steered towards a given target, then corroborate and extend our analytical results with computational experiments and a study of optimal controls. I will highlight the advantages and disadvantages of each approach, as well as propose several directions for future research. 

If time permits, I will also discuss recent work on introducing ageing effects, which allows us to explore the mean-field limit and long time behaviour of these models, beyond just reaching consensus. 

This event is supported by CIM.