Singularities/Varieties with Singularities

Algorithmic Desingularization:

  • Algorithms and Applications in Characteristic zero
  • Experiments and Phenomena in positive Characteristic
  • Regular and Canonical Models for Families of Curves over the Integers
  • Order zeta functions for number rings via simultaneous monomialization

Classification and Invariants of Singularities:

  • Complete Intersections
  • Cohen-Macaulay Case
  • Determinantal Singularities

Computer Algebra

Parallel Algorithms in Algebraic Geometry

Technical Applications