Research

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