TEORÍA DE SINGULARIDADES


Our research involves the study of singularities in algebraic and analytic geometry. Specific topics are the vanishing cohomology with D-module and Hodge structure and a similar study of vanishing rational homotopy of singularities), the topology of the Milnor fibrarion and the link, equisingularity, resolution and local uniformisation in characterisric 0 and p (including algorithmic aspects), invariants of surface singularities and of complex analytic spaces and their connection with gauge theory (including applications to clasical problems of rational cuspidal curves such as Coolidge-Nagata problem), and the structure of arcs spaces and motivic invariants, and their relation with resolution. Recently we are exploring also connections with tropical and non-arquimedean geometry (which links with number theory problems such as Igusas conjecture and with our study on arc spaces), with Donaldson-Thomas invariants and enumerative geometry and relations with contact and symplectic geometry.

Especialización principal

Área científica:
Disciplina ERC:
  • PE - DOMAIN PHYSICAL SCIENCE AND ENGINEERING
  • PE1 Mathematics
Industrial Leadership:
  • 7. Other
  • 7.1. Other
Societal Challenges:
  • 7. Other
  • 7.1. Other