Teissier, Bernard; Matematični kolokvij november 2013

Some recent developments around the Łojasiewicz inequality

Bernard Teissier

Institut de Mathématiques de Jussieu, Paris

14. november 2013

The Łojasiewicz inequality states that if a real (sub)analytic function f on an open set U of ${\mathbf R}^n$ vanishes on the zero set of another (sub)analytic function g, then there is a reason: for every compact subset K of U, there exist C > 0 and θ > 0 such that on K we have $\vert f\vert . This has had many resonances in analysis, algebra, algebraic geometry. I will describe some of them, as well as some properties of the best possible exponent θ and its relation with the geometry of the map $(f,g)\colon U\to \mathbf R^2$.