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 12:0013:00 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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