Mathematical molecular biosciences and biophysics: Differential geometry based solvation models; Variational multiscale models for ion channel transport; Density functional theory (DFT) of proton transport; Curvature based biomolecular surfaces; Multiscale virus capsid modeling; Geometric modeling of protein complexes; Mechanoelectrical transducers; Flexibility-rigidity index (FRI) for biomolecules; Stochastic B-factor prediction; Topological fingerprints of biomolecules; Electrostatic binding analysis; Reeb graph based protein pocket detection; Protein-ligand binding affinity; Partition coefficients; Toxicity prediction; Mutation induced protein folding stability change.
Machine learning, big data, and bioinformatics: Deep learning; Topological learning; Multiscale manifold regularization; Topological data analysis; Champion; Persistent homology; de Rham-Hodge theory, PDE transform; Parametrization via convex optimization; Machine learning.
Systems biology and quantitative systems pharmacology: Integrating systems biology, biomechanics, physiology and clinical trial data to predict drug pharmacokinetics, pharmacodynamics and pharmacometrics.
Biomedical image and surface analysis: Geometric flow approaches to images and surfaces; PDE transform; Image edge analysis by coupled PDEs; Bioluminescence tomography.
High order interface methods: Matched interface and boundary (MIB); Multidomain interface problems.
Nano modeling and simulation: Nano-electronic devices; Nanofluidic systems.
Quantum kinetic theory: Quantum Boltzmann theory; Transport theory; Reaction rate theory.
Wavelet local spectral methods and applications: Computational electromagnetics; Computational fluid dynamics; Richtmyer-Meshkov instability; Structural stability analysis.
Dynamical systems: Controlling chaos; Controlling turbulence; Controlling pattern formation.