Universität Konstanz Fachbereich Mathematik und Statistik Schwerpunkt Reelle Geometrie und Algebra Einladung Im Oberseminar Reelle Geometrie und Algebra hält Grey Violet (Universität Konstanz) am Freitag, 12.02.2016, einen Vortrag zum Thema: Topology of root clustering problems Der Vortrag findet um 13:30 Uhr in F426 statt. Alle Interessenten sind herzlich eingeladen. Abstract: It is known that the space of univariate monic hyperbolic polynomials of degree n is homeomorphic to R × Rn−1 + . Notion of hyperbolicity is one of the many possible notions concerning different distributions of a root of polynomial with respect to some set Ω, which for the hyperbolic case is the real line. Those notions are usually called stability conditions (or root clustering problems), among them one could note such conditions as Hurwitz stability for characteristic polynomial of linear ODE, Schur stability for linear difference equations, pole placement problems and many others. Our goal is to describe topology of the sets of polynomials with fixed distribution of roots relative to the Ω, adjacencies between these sets and to provide an explanation for the special position of hyperbolicity, Hurwitz and Schur stabilities. Sebastian Gruler Koordinator Oberseminar
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