I am mainly interested in extremal and probabilistic combinatorics. I also enjoy spectral graph theory and analysis. I’m a firm believer in the experimental side of theoretical mathematics. Much of my work is aided by code I write, especially in sage. You may also read my research statement and CV.
My dissertation work revolves around the edit distance problem. Informally we ask, “How much work is needed to remove a fixed graph from an arbitrary host graph?”. Stated differently, fix some graph F. What is the maximum proportion of edits (edge-additions and edge-deletion) that must be made to an arbitrary graph G to ensure that G contains no induced copy of F? I gave a talk at the USC Discrete Mathematics seminar on the case where the “fixed” graph F is an Erdős–Rényi random graph.
Jane Breen, Alex W. N. Riasanovsky, Michael Tait, John Urschel, Maximum spread of graphs and bipartite graphs (submitted, 2021). arXiv
Ryan R. Martin, Alexander W. N. Riasanovsky, On the edit distance function of the random graph Combinatorics, Probability and Computing (2021), 1-23. arXiv
Jane Breen, Steve Butler, Melissa Fuentes, Bernard Lidický, Michael Phillips, Alexander W. N. Riasanovksy, Sung-Yell Song, Ralihe R. Villagrán, Cedar Wiseman, Xiaohong Zhang, Hadamard diagonalizable graphs of order at most 36 (under review, 2020). arXiv
Steven N. Harding, Alexander W. N. Riasanovsky, Moments of the weighted Cantor measures, Demonstr. Math., 52 (2019), no. 1, 256-273. arXiv
András Gyárfás, Alexander W. N. Riasanovsky, Melissa U. Sherman-Bennet, Chromatic Ramsey numbers of acyclic hypergraphs, Discrete Math., 340 (2017), no. 3, 373-378. arXiv
Alex Collins, Stanislaw Radziszowski, Alexander W. N. Riasanovsky, John C. Wallace, Zarankiewicz numbers and bipartite Ramsey numbers, Journal of Algorithms and Computation, 47 (2016), no. 1, 63-78. arXiv
Joshua N. Cooper, Alexander W. N. Riasanovsky, On the reciprocal of the binary generating function for the sum of divisors, J. Integer Seq., 16 (2013), no. 1, Article 13.18, 13 pp. arXiv