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The Flow of Polynomial Roots Under Differentiation - SIAM PDE Seminar

Offered By: Society for Industrial and Applied Mathematics via YouTube

Tags

Partial Differential Equations Courses Mathematical Analysis Courses Complex Analysis Courses Mathematical Biology Courses

Course Description

Overview

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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

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