Applied Analysis Seminar

Wednesday September 24 in K9509, SFU
2:30-3:30

Adrian Lewis
Simon Fraser University,

Title: "Nonsmooth Lojasiewicz inequalities"

Abstract: Consider a real-analytic function f on a Euclidean space, and suppose f(0)=0. The Lojasiewicz gradient inequality asserts the existence of a positive exponent a<1 such that

|f(x)|^a
--------
|f'(x)|

is bounded above near 0. It is a crucial tool in a recent proof of the famous "gradient conjecture of Thom", that steepest descent trajectories for real-analytic functions do not oscillate near critical points. I will outline some nonsmooth variants. This is joint work with Jerome Bolte and Aris Daniilidis.