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Development and analysis of such models for problems arising in neuroscience and, as time permits, fluid dynamics mathematical modeling and analysis techniques which can be applied to problems from engineering, physics, chemistry, and biology.

• Neuroscience Modeling
• conductance-based neuron models, such as the Hodgkin-Huxley equations
• simple reductions of conductance-based neuron models
• nullcline analysis of neuron models
• integrate-and-fire neuron models
• phase response curves and isochrons for periodically firing neurons
• dynamics of coupled neurons
• reduction of coupled neuron systems to phase models
• analysis of phase-locked solutions for coupled neuron systems
• analysis of bursting neuron models
• Fluid Dynamics Modeling
• basics of fluid dynamics
• derivation of low-dimensional models using Galerkin projection
• analysis of the Lorenz equations for fluid convection, a prototypical chaotic system
• analysis of a model for shear flow turbulence derived using Galerkin projection
• basics of center manifold reduction
• derivation of low-dimensional models using symmetry methods
• analysis of a model for binary fluid convection derived using symmetry methods
• derivation of low-dimensional models using the proper orthogonal decomposition
• analysis of a model for shear flow turbulence derived using the proper orthogonal decomposition
• pseudospectra analysis of linear models for shear flow turbulence
•  Classifier Type: Decision Trees, Discriminant Analysis, Logistic Regression, SVM Support Vector Machines, Nearest Neighbor, Ensembles