Rombach's research bridges gaps between the pure and applied sides of graph/network theory. Sample areas of interest for Rombach include graph coloring, random graphs, algorithms and complexity, graph representations of matroids, crime network modeling, and core-periphery/centrality detection in networks. Prior to UVM, Rombach was an assistant adjunct professor at UCLA, working with Andrea Bertozzi. Rombach earned her Ph.D. at the University of Oxford in 2013, under the supervision of Mason Porter and Alex Scott.