Research
Faculty Research
Human-Computer Interaction (HCI), Multimedia Data Analysis, Multimedia Systems, Multimodal Interfaces, Information Visualization and Interactions, UI/UX Design and Evaluation, Machine Learning
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.
Combinatorial Geometry (Polytopes) and Rigidity Theory
Mathematics Education
Algebraic combinatorics, particularly enumerative problems underlying questions in geometry and representation theory
Network Science, Bioinformatics, Knowledge Graphs, Graph Neural Networks, Explainable AI
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 Algebras, Homological Algebra), Analysis (operator theory, free probability)
Numerical software for the computation of error-controlled solutions of systems of initial value and boundary value ordinary differential equations and parabolic partial differential equations, Runge-Kutta methods, collocation methods.
Computer graphics, Computer vision, Point cloud processing, Geometric deep learning, Spatial data structures
Number theory: circle packings, continued fractions, quaternion algebras, and computations.
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).