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.