Faculty Research Areas

• Algebraic combinatorics
• Algorithmic learning theory
• Application of wavelets to deconvolution problems in antenna data analysis
• Applied mathematics
• Calculus of Variations
• Classical knot theory, topology and geometry of 3-manifolds, algebraic topology based on knots, secondary: Graph theory, hyperbolic geometry, 4-manifolds, statistical mechanics, representations of Lie algebras and Hopf algebras (quantum groups), Hecke algebras, character varieties, symplectic structures, Hochschild homology, cyclic homology, distributive homology, entropic magmas,, Yang-Baxter homology, (co)cycle invariants of links
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• Combinatorics
• Computability and computational complexity theory
• Computable model theory
• Computational Fluid Dynamics
• Computational Linear Algebra
• Computers in mathematics research
• Conformal mapping theory and elliptic functions
• Equilibrium statistical physics
• Ergodic theory and dynamical systems
• Functional Analysis
• Graph theory
• History of mathematics
• Khovanov-Rozansky homology
• Launch dynamics of large scientific balloons
• Math and art
• Math and music
• Math and politics
• Mathematical logic
• Mathematical problems
• Mathematics Education
• Micro-phase separation of di-block copolymers; self-organizing inhibitory systems
• Nonlinear partial differential equations with applications to lightweight inflatable structures, including large scientific balloons, aerostats, antennas, aerodynamic decelerators, large-aperture reflectors
• Numerical Analysis
• Partial Differential Equations
• Phase separation and phase transformation in physical and biological systems
• Quantum computing
• Social science mathematics;
• Teaching Mathematics to gifted children
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