AMS-Simons Grant Supports Opinion Dynamics Research

Large networks of interacting particles or agents are ubiquitous in biological and social systems, yet understanding their dynamics can be analytically and computationally challenging. Harvey Mudd College mathematics professor Heather Brooks sees recent advances in graph limits as providing a promising avenue for studying such systems.

Brooks, assistant professor of mathematics and Barbara Stokes Dewey Assistant Professor of Life Sciences, recently received the American Mathematical Society Simons Research Enhancement Grant for Primarily Undergraduate Institution Faculty to support her project “Using Continuum Models to Understand Opinion Dynamics on Networks.” This highly competitive national award, funded by the American Mathematical Society and the Simons Foundation, provides $3,000 per year for three years to research-related activities plus an additional $300 per year toward the grantee’s department and another $300 per year for administrative costs.

“Using a class of opinion dynamics models developed to analyze the mechanisms behind consensus and polarization, my collaborators and I will employ graph limits to explore the asymptotic behavior of opinion states observed in the continuum limit as compared to what is observed in large but finite networks,” says Brooks, who joined the Harvey Mudd faculty in 2020. 

Brooks will investigate when graphons can accurately approximate opinion clusters and positions in large random network models, then apply these continuum limits to detect bifurcations between consensus and polarization in the sigmoidal bounded-confidence model.

While Brooks’s work focuses on opinion dynamics as an application, these methods may also be useful in other biological and ecological contexts that involve many interacting agents with underlying interactions, like tracking disease spread, understanding collective animal behavior or studying how large populations of neurons interact to coordinate brain activity.

Funding for this project will advance work on this project by supporting Brooks’ visits to work with collaborators in London and Philadelphia and her presentations of the work at the Joint Mathematical Meetings and Society for Industrial and Applied Mathematics conference.