Research

My research is in combinatorics and graph theory. In particular, my work uses probabilistic methods and spectral graph theory to understand the structure of graphs.

My doctoral advisor was Paul Horn at the University of Denver.

Publications

• Gradient and Harnack-type estimates for PageRank, Network Science (2020), 1-19. (Joint with P. Horn)

• A Gradient Estimate for PageRank, Proceedings of the Eighth International Conference on Complex Networks and Their Applications. (Joint with P. Horn)

• Color-blind index in graphs of very low degree, Discrete Applied Mathematics (2017), 225:122-129. (Joint with J. Diemunsch, N. Graber, L. Kramer, V. Larsen, L.L. Nelsen, D. Sigler, D. Stolee and C. Suer)

• An integral formula for counting perfect matchings in graphs, Pi Mu Epsilon Journal (2013) 13:9:541-548. (Advised by P.M. Kayll)

Submitted Papers

• Ranking Politicians in Colorado Using Google's PageRank Algorithm. (Joint with L.L. Nelsen)

• Domino Antimagic Squares and Rectangles. (Joint with A.M. Marr, L.L. Nelsen, C. Osborne, and V. Vasilevska)

• Many edge-disjoint rainbow spanning trees in general graphs, preprint. (Joint with P. Horn)

• Erdős-Szekeres on-line, preprint. (Joint with K. Boyer, L.L. Nelsen, F. Pfender, E. Reiland, and R. Solava)