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X-WR-CALDESC:FAU DCN-AvH. Chair for Dynamics, Control, Machine Learning and Numerics -Alexander von Humboldt Professorship
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DTSTART;TZID=Europe/Berlin:20210113T160000
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DTSTAMP:20211020T084515Z
CREATED:20211020
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SUMMARY:A PDE describing Roots of Polynomials under Differentiation
DESCRIPTION:Speaker: Prof. Dr. Stefan Steinerberger\nAffiliation: University of Washington, USA\nRequest Zoom meeting link\nAbstract. Suppose you have a polynomial p_n (think of n as being quite large) and suppose you know where the roots are. What can you say about the roots of the derivative p_n’? Clearly, one could compute them but if n is large, that is not so easy — can you make a softer statement, predicting “roughly” where they are? This question goes back to Gauss who proved a pretty Theorem about it. We will ask the question of what happens when one keeps differentiating: if the roots of p_n look like, say, a Gaussian, what can you say about the roots of the polynomial after you have differentiated 0.1*n times? This leads to some very fun equations and some fascinating new connections to Probability Theory, Potential Theory and Partial Differential Equations. In particular, there is a nice nonlocal PDE that seems to describe everything. I promise nice pictures!\n
URL:https://dcn.nat.fau.eu/events/a-pde-describing-roots-of-polynomials-under-differentiation/
CATEGORIES:FAU CAA Seminar
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