One of my research areas is connected to blocking sets of finite projective spaces. When the size of a blocking set is small, then the Linearity Conjecture states that it has to be a linear point set, or possibly the union of linear point sets. In some special cases the Linearity Conjecture has already been proved, and there are some further cases where there is hope to prove it.

Another area of research is connected to stability of blocking sets. Here we are trying to prove that if a point set is close to being a blocking set (ie. almost blocking all hyperplanes/k-subspaces), then it can be obtained from a blocking set by removing only a few points. For proving such results algebraic methods can be used, such as the inspection of the Redei polynomial of the point set.