My main research areas are convex and combinatorial geometry and category theory, I have also written research papers in statistics, computer science, elementary number theory, homology theory, topology, and the history of math textbooks.
Graph Theory, Well-Covered graphs, Domination in Graphs, Planar Triangulations, Network security
Combinatorial Geometry (Polytopes) and Rigidity Theory
Random matrices, Integrable Systems, Analysis of integrable dispersive PDEs. Riemann-Hilbert problems, Deep Learning theory, Optimization.
Algebraic combinatorics, particularly enumerative problems underlying questions in geometry and representation theory
Complex Networks, Bioinformatics, Wireless Mesh Networks, Network Coding
Preliminary test estimator, James-Stein estimator, and their improved versions. The performances of these estimators are compared to the usual estimators in various situations and problems through biases, mean squares errors, and risk functions.
Formal language and automaton theory, decidability, complexity, coding theory, DNA computing
Data Mining, Artificial Intelligence, Soft Computing, Fuzzy Sets, Rough Sets, Information Retrieval.
Algebra (Hopf Algebra, Homological Algebra), Analysis (operator theory, free probability)
Numerical solution of ordinary differential equations, Runge-Kutta methods, and the adaptive method-of-lines for the numerical solution of partial differential equations.
Set Theory, Mathematical Logic
Dr. Scobey wrote Pascal and C++ lab manuals used in first-year courses for many years; started annual High School Programming Competition in 2000; developed an extensive website for use as a C++ STL reference; received Father William A. Stewart, S. J., Medal for Excellence in Teaching (2004); co-authored a university text on web programming published by Jones and Bartlett (2012).
Computer graphics, Computer vision, Point cloud processing, Geometric deep learning, Spatial data structures
Human-Computer Interaction (HCI), Multimedia Data Analysis, Multimedia Systems, Multimodal Interfaces, Information Visualization and Interactions, UI/UX Design and Evaluation, Machine Learning