### Thursday 12 March 2015 from 12:00–13:00 in Carslaw 535A

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

Laurentiu Paunescu (Sydney)

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.