In this paper we present some new results in the deformation theory of plane curve singularities. The methods rely on the study of analytic properties of linear non homogeneous ODE’s.

In this paper, we use topological methods to study various semicontinuity properties of the local spectrum of singular points of algebraic plane curves and spectrum at infinity of polynomial maps in… (More)

We use Morse theory arguments to study links of algebraic curves. Looking at the signature of links of intersection of an algebraic curve C with spheres of growing radii we find some new criteria… (More)

We apply the methods of Heegaard Floer homology to identify topological properties of complex curves in CP2. As one application, we resolve an open conjecture that constrains the Alexander polynomial… (More)

We compute ρ–invariant for iterated torus knots K for the standard representation π1(S \ K) → Z given by abelianisation. For algebraic knots, this invariant turns out to be very closely related to an… (More)

We prove a quadratic in m and n estimate for the maximal number of limit cycles bifurcating from a focus for the Liénard equation x+f(x) _ x+ g(x) = 0; where f and g are polynomials of degree m and… (More)

An immersed concordance between two links is a concordance with possible self-intersections. Given an immersed concordance we construct a smooth fourdimensional cobordism between surgeries on links.… (More)