For my thesis work, I use techniques from topological combinatorics to solve a problem in group theory. To each finite group G there is an associated simplicial complex In(G) which arises from minimal generating sets for subgroups of G. In low dimensions, we can visualize these with the help of computer algebra systems.

I generate these complexes in GAP and use this data in Polymake to generate images that display the orbits of the complexes under the action of the automorphism group of G.

Pictured is the resulting image for the independence complex of the direct product of the cyclic group C₃ and the quaternion group Q₈.