Hybrid seminar at McGill University or Zoom.

This talk overviews my recent work on pattern formation, persistence, and stability in dynamical systems on large random networks using graphons as continuum limits. I will show how graphon Laplacians provide a tractable framework for analyzing Turing type instabilities and pattern forming bifurcations, yielding rigorous connections between continuum spectra and bifurcations in finite graphs with high probability. I will then discuss persistence results showing that nondegenerate steady states of graphon dynamical systems and their linear stability persist in sufficiently large random network realizations. Finally, I will highlight recent results on synchronization in random oscillator networks, where a graphon formulation of the Kuramoto model identifies critical coupling thresholds and bifurcations to synchronized states that accurately predict behaviour in large finite networks.

Biography: Jason Bramburger is an assistant professor of mathematics at Concordia University. Previously, he was an NSERC postdoctoral fellow at Brown University, a PIMS postdoctoral fellow at the University of Victoria, and a member of the Brunton-Kutz research group at the University of Washington. In 2021 he was named a fellow of the Institute of Advanced Study in Guildford, UK. His mathematical expertise is in dynamical systems, which he applies broadly to problems in pattern formation, wave propagation, spatiotemporal chaos, and data science. Jason has a passion for outreach and effective communication, as demonstrated by expository articles and an active YouTube channel with course lectures on differential equations, mathematical modeling, and dynamical systems.