Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic ...

My research has been mainly in algebraic geometry, with an abiding interest in the study of algebraic cycles, particularly in the presence of singularities. I have established a number of results in ...

One of the bigger questions within algebraic geometry is how to “resolve” singularities — that is, how to get rid of them. Mathematically, resolving a singularity means smoothing over the ...

Variants of this appear in several mathematical disciplines. In algebraic geometry, $\mathfrak{M}_g$ is constructed using geometric invariant theory and has a well-studied compactification introduced ...

Poisson geometry, the mathematics of classical and quantum fields, and PDE's coming from Physics. Active research includes the study of topological effects and singularities when quantizing classical ...