Research

My area of research is at the intersection of singularity theory and algebraic geometry. More precisely I study the subjects of

• valuation theory: key polynomials and how they help to parametrize valuative trees. I am also interested in their use in attacking the local uniformization problem. I seek to encode the data the key polynomials hold into ultrametric objects.

• numerical control of curve singularities in families: given a one parameter family X (i.e. a flat morphism from X to a small complex disc D) one wishes to study how numerical information (Milnor or Tjurina numbers, multiplicities etc.) vary when specializing. The discontinuities of these invariants encode information necessary for equisingular classification.