Linear algebra, matrix analysis, especially the theory of nonnegative matrices and their generalizations. Particular interests include the numerical range; graphs associated with matrices; matrix patterns over rings and finite fields; numerical linear algebra; applications in dynamical systems, data analysis and machine learning.
Cryptography/Cryptanalysis, number theoretic transforms relating to coding theory, and understanding the threat/hype/furor of Cryptographically Relevant Quantum Computers (CRQC) on existing algorithms
Number Theory and Combinatorics
Secure Authenticated Key Exchange
Prime Proof Protocol
MATHEMATICAL MODELING – Pattern Formation, Contaminant Transport, Spread of Diseases, Population Models & Solitons;COMPUTATIONAL MATHEMATICS – Finite Element/Finite Difference methods, Spectral methods, Operator Splitting methods, Iterative methods & Machine Learning;MATHEMATICS LEARNING – Interactive online lessons & Evidence-based Experiential learning
Fluid and Solid Mechanics
Analysis and PDEs
Modeling the Spread of COVID-19 in Enclosed Spaces
Analysis of a population model with advection and an autocatalytic-type growth
Eventually nonnegative matrices, nonnegative matrices, M-matrices, inverse eigenvalue problem, spectrally arbitrary patterns.
Linear algebra, matrix analysis, especially the theory of nonnegative matrices and their generalizations. Particular interests include the numerical range; graphs and patterns associated with matrices; numerical linear algebra; applications in dynamical systems, control theory, data analysis, machine learning and artificial intelligence.
The Fiber of P-matrices