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kranich-ws16

Contact

Carl von Ossietzky Universität Oldenburg
Institut für Mathematik
26111 Oldenburg
olfy1qucry1foptb7pl@uogvl.wppdeqjx

Coordinators

Prof. Dr. Florian Hess
flom97dgrianei.hess@uol.do462e<br />3zgu (florxuqzian.hesn7ms@ulzuol.dt9wbme)Phone: +49 (0) 441 798-2906


Prof. Dr. Andreas Stein
andctfreauw2hs.stein@uol.de<brtr />tvpbn (anz/uxdruwkxeas.stein@uoxpt4l.5h8kgdekhrx)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.

Wet/jbmastqet2erjpwj (internkuyret@uol.deevl5o) (Stand: 07.11.2019)