Springe direkt zu Inhalt

Mathe. Kolloquium: Prof. Elias Wegert (Freiberg) "Exploring Complex Functions Using Phase Plots"

11.02.2016 | 17:15


Graphical visualization of functions is one of the most powerful tools in (applied) mathematics. While pictorial representations of real functions are widely used for centuries, representations of complex (analytic) functions are not so common. As a counterpart of the traditional ``analytic landscapes'', the talk promotes special color-representations, so-called ``phase plots'', depicting a function $f$ directly on its domain by color-coding the argument (or phase) of $f$. The image shows a phase plot of a finite Blaschke product.

Phase plots are like fingerprints: though part of the information (the modulus) is neglected, meromorphic functions can be uniquely reconstructed from their phase plots up to a positive constant factor. Moreover, several modifications allow one to incorporate additional information.

In the talk we explain how basic properties of a function can be recovered from its phase plot, show images of special functions,  and present applications in teaching and research: the argument principle and its extension, universality of the Riemann zeta function, and the discovery of a stochastic periodicity in its phase plot


ab  16:45 Uhr,

Arnimallee 3,  Raum 006


Koordinator:  Prof. Dr. Alexander Schmitt


Zeit & Ort

11.02.2016 | 17:15

Hörsaal 1
Arnimallee 3
14195 Berlin