Research
My research interests are in topological graph theory, especially graph embeddings, orientable genus, rotation systems, and forbidden minors.
I show that the genus polynomial of a 2-connected cubic graph depends only on its cycle matroid, and that the adjacency spectrum and the genus polynomial do not determine each other. I also computed it for all 7,875,918 connected cubic graphs through 22 vertices.
Alexander Metzger and I wrote PAGE, an algorithm that computes the orientable genus of a connected graph by searching over its rotation systems. We used it to show that the (3,12)-cage has genus 17, and it is now in SageMath.
My undergraduate honors thesis, advised by François Clément, on embedding graphs on surfaces. The later sections cover PAGE and the forbidden toroidal minors.