Research

Here are some of the subjects I have worked on.

In general, I am interested in discrete Mathematics, in particular polyhedral combinatorics, combinatorial optimization and graph theory.

I am very interested in Minkowski sums of polytopes, which I have studied for my PhD thesis. Minkowski sums have countless applications, and their combinatorial properties have been little studied so far.

My interest in Minkowski sums has led me to looking for counter-examples to the Hirsch conjecture. The results of my research are here.

I am currently working on multicommodity flows.

I am also working on the 3D visibility skeleton, which is a data structure encoding visibility information for a set of given scene objects. Roughly speaking, the visibility skeleton data structure partitions line space into connected components such that the set of line segments in the same component are tangent to the same objects.