Date/Time Date(s) - 16/01/20253:30 pm - 4:30 pm
Dr. Henry Schenck R.K. Brown Chair of Mathematics, Auburn University Research Area: Algebra
Title: Dynamical Systems: Synchronizing Fireflies Meet the Segre Variety
Abstract: When does a system of coupled oscillators synchronize? This central question in dynamical systems arises in applications ranging from power grids to neuroscience to biology: why do fireflies sometimes begin flashing in harmony? Perhaps the most studied model is due to Kuramoto (1975). In this talk, we’ll study the Kuramoto model from an algebraic viewpoint by translating the dynamics of a system of trigonometric ODE’s into algebraic equations. This enables us to identify network (graph) topologies that exhibit unexpected behaviors, such as identifying positive dimensional components in the set of potential solutions (e.g. curves instead of points). The talk will include a surprising (at least to us!) connection to Segre varieties.