The Flow of Polynomial Roots Under Differentiation - SIAM PDE Seminar

Explore the fascinating world of polynomial root dynamics in this one-hour seminar presented by Alexander Kiselev from Duke University. Delve into the classical question of how polynomial roots move under differentiation, tracing contributions from mathematical luminaries such as Gauss, Lucas, Marcel Riesz, and Polya. Discover Stefan Steinerberger's groundbreaking 2018 derivation of a partial differential equation (PDE) describing root dynamics, drawing intriguing parallels to hydrodynamic models used in mathematical biology for collective behavior and flocking. Examine the challenges in proving global regularity for this critical, strongly nonlinear equation, and learn about recent advancements in establishing global regularity and connecting solutions to root evolution in trigonometric polynomials. Gain insights into cutting-edge research in this field, presented as part of the Society for Industrial and Applied Mathematics' initiative to promote mathematical discourse during the COVID-19 pandemic.