Thursday 12 March 2015 from 12:00–13:00 in Carslaw 535A
Please join us for lunch at the Grandstand after the talk!
Abstract: The level curves of an analytic function germ can have bumps (maxima of Gaussian curvature) at unexpected points near the singularity. This phenomenon is fully explored for \[f(z,w)\in \mathbb{C}\{z,w\}\] using the Newton-Puiseux infinitesimals and the notion of gradient canyon. Equally unexpected is the Dirac phenomenon: as \(c\to 0,\) the total Gaussian curvature of \(f=c\) accumulates in the minimal gradient canyons, and nowhere else. Our approach mimics the introduction of polar coordinates in Analytic Geometry.
This is joint work with S. Koike and T-C Kuo.
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