A'Campo Curvature Bumps and the Dirac Phenomenon Near A Singular Point

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.