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kranich-ws16

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Carl von Ossietzky Universität Oldenburg
Institut für Mathematik
26111 Oldenburg
olcryamux/pt@uol/db0.dri5pwe+7sn

Coordinators

Prof. Dr. Florian Hess
flo3xjqdrian.hub3ress@qcnuol.de<vl0fbr />kumn (florian.adhhthejh8grss@uol.desv)Phone: +49 (0) 441 798-2906


Prof. Dr. Andreas Stein
andrnjx5eaq1s.sahc6tein@uooqnl.dentui<brbvoqf /> (anvd7fdrearoek0s.stay6ein@+iixwuol.dewx)Phone: +49 (0) 441 798-3232

Talk

Stefan Kranich (TU München)

26.01.2017 - W01 0-012 (Wechloy), 16 Uhr 

An epsilon-delta bound for plane algebraic curves

Abstract: Given a plane algebraic curve C: f(x, y) = 0, x_1 ∈ ℂ not a singularity of y w.r.t. x, and ε > 0, we can compute δ > 0 such that |y_j(x_1) - y_j(x_2)| < ε for all holomorphic functions y_j(x) which satisfy f(x, y_j(x)) = 0 in a neighbourhood of x_1 and for all x_2 with |x_1 − x_2| < δ. 

We discuss this result and two applications: Firstly, algorithms for reliable homotopy continuation of plane algebraic curves and systems of plane algebraic curves; secondly, a GPU-based algorithm for visualization of algebraic Riemann surfaces.

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