The Flow of Polynomial Roots Under Differentiation - SIAM PDE Seminar
Offered By: Society for Industrial and Applied Mathematics via YouTube
Course Description
Overview
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.
Syllabus
Seminar In the Analysis and Methods of PDE (SIAM PDE): Alexander Kiselev
Taught by
Society for Industrial and Applied Mathematics
Related Courses
Insect Outbreak Model - A Cusp Catastrophe Population Dynamics ExampleRoss Dynamics Lab via YouTube Why There Are No Three-Headed Monsters
University of Oxford via YouTube Turing's Reaction-Diffusion System and Agent-Based Models in Biology - Lecture 2
International Centre for Theoretical Sciences via YouTube Cargo Transport in Vivo - How Is Transport Regulated? by Steven P. Gross
International Centre for Theoretical Sciences via YouTube The Motion of Hybrid Zones - And How to Stop Them
International Mathematical Union via YouTube