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)

# 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

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.