Maciej Borodzik

University of Warsaw

Codimension of a singular point and related topics

Beginning with an elementary introduction I will sketch a very intuitive definition of a codimension of a singular point of a plane curve. I will show some simple examples, then turn to the question of global estimates. I will explain, how various questions about the properties of codimension naturally arise in different fields of mathematics, such as affine algebraic geometry, singularity theory and ordinary differential equations (via the XVI. Hilbert problem).

There are also several attempts of answering this questions, I will discuss if time allows three approaches: one of them is by topology of algebraic surfaces (real 4-dimensional manifolds), the second one is via knot theory and the third one via elementary theory of ODE's.