In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose roots (zeros) are located in the left half-plane of the complex plane or on the imaginary axis, that is, the real part of every root is zero or negative. Such a polynomial must have coefficients that are positive real numbers. The term is sometimes restricted to polynomials whose roots have real parts that are strictly negative, excluding the imaginary axis (i.e., a Hurwitz stable polynomial). A polynomial function P(s) of a complex variable s is said to be Hurwitz if the following conditions are satisfied: 1. P(s) is real when s is real.2. The roots of P(s) have real parts which are zero or negative. Hurwitz polynomials are important in control systems theory, because they represent the characteristic equations of stable linear systems. Whether a polynomial is Hurwitz can be determined by solving the equation to find the roots, or from the coefficients without solving the equation by the Routh–Hurwitz stability criterion. (Wikipedia).
David Roberts, Hurwitz Belyi maps
VaNTAGe seminar, October 12, 2021 License: CC-BY-NC-SA
From playlist Belyi maps and Hurwitz spaces
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From playlist Control Theory
John Voight, Belyi maps in number theory: a survey
VaNTAGe Seminar, August 17, 2021 License CC-BY-NC-SA
From playlist Belyi maps and Hurwitz spaces
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EE102: Introduction to Signals & Systems, Lecture 22
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From playlist EE102: Introduction to Signals & Systems
Jeremy Booher, Can you hear the shape of a curve
VaNTAGe seminar, on Nov 24, 2020 License: CC-BY-NC-SA.
From playlist ICERM/AGNTC workshop updates
David Zureick-Brown, Moduli spaces and arithmetic statistics
VaNTAGe seminar on March 3, 2020 License: CC-BY-NC-SA Closed captions provided by Andrew Sutherland.
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VaNTAGe seminar, September 21, 2021 License: CC-BY-NC-SA
From playlist Belyi maps and Hurwitz spaces
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From playlist Classify Polynomials | Simplify First
[BOURBAKI 2019] Homology of Hurwitz spaces and the Cohen–Lenstra (...)- Randal-Williams - 15/06/19
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From playlist BOURBAKI - 2019
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