Stefan Helmke is working on algebraic geometry.
His main interest is the study of base points
of linear systems. It has been conjectured, that
the existence of such base points always have a
geometric reason, namely it should imply the
existence of subvarieties of very small degree
containing the base point. A special case of this
conjecture is the famous Fujita Conjecture.
Another research interest is the relation between deformations of singularities and certain groups, generalizing a celebrated construction due to E. Brieskorn, A. Grothendieck and P. Slodowy. This construction was successfully worked out in the case of simple elliptic singularities of degree up to 4. Recently, the construction was extended to degrees 5 and 6, which are not complete intersections.