Joshua Ducey

Joshua Ducey is a Professor of Pure Mathematics in the Department of Mathematics & Statistics at James Madison University (JMU), where he has served since 2011. His research focuses on algebraic combinatorics, particularly applying representation theory to compute invariants of combinatorial structures like Smith normal forms of incidence matrices. He holds a PhD (2011), MS (2007), and BA (2005) in Mathematics from the University of Florida and University of Richmond, respectively.

His work spans topics including critical groups of graphs, strongly regular graphs, and combinatorial matrix theory. Notable contributions include studies on Kneser graphs, Grassmann graphs, and Rook's graphs. He has advised numerous undergraduate research projects, mentoring students on topics ranging from clique regular graphs to Rota's Basis Conjecture.

Dr. Ducey co-directs the Shenandoah Undergraduate Mathematics and Statistics Conference (SUMS) and has presented at conferences such as the AMS Sectional Meetings and the University of Hawaii. His research emphasizes interdisciplinary connections, blending algebraic techniques with combinatorial problems.

Through collaborative projects, he has explored open problems in graph theory, such as Conway's 99-graph problem, and contributed to the understanding of invariants like Smith groups and critical groups across diverse graph families.