**SMS scnews item created by Stephan Tillmann at Mon 9 Mar 2015 1259**

Type: Seminar

Distribution: World

Expiry: 8 Jun 2015

**Calendar1: 12 Mar 2015 1200-1300**

**CalLoc1: Carslaw 535A**

Auth: tillmann@p710.pc (assumed)

### Geometry-Topology-Analysis Seminar

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

### Laurentiu Paunescu

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.