Oswin Aichholzer is interested in data structures and algorithms, combinatorial geometry, in particular discrete and computational geometry, graph algorithms and enumerative algorithms.
He especially works on combinatorial structures behind point sets ((abstract) order types) and topological drawings of graphs ((abstract) rotation systems) and their relation to other structures. He also intensively published on triangulations, pseudo-triangulations and other geometric structures. Recently he investigated explicit combinatorial bijections between plane matchings and triangulations of (colored) convex sets, related to Temperley-Lieb algebras. The resulting explicit bijection is also related to the Tamari lattice, but different from what has been obtained from there.