Faculty

• Machine learning and data science
• System identification and reduced-order modeling
• Optimization and optimal control
• Hamiltonian/Lagrangian dynamical systems
• Stochastic processes
• Scientific computing

Professor Blanchette is an applied mathematician primarily interested in problems involving fluid dynamics. A large portion of his research is concerned with problems related to sedimentation. The accumulation patterns, erosion potential and transport properties of such systems are of geophysical and environmental interest. He also studies systems where two immiscible fluids are present and surface tension plays a significant role, such as drops, bubbles and micro-fluidic devices. Professor Blanchette's approach is mostly theoretical and numerical, and he also values interactions with experimentalists so as to paint as complete a picture as possible of a given physical system.

Professor Ilan's research interest lies in the mathematics involved with real-world phenomena, and its application to areas such as the control of intense lasers beams and harvesting solar energy. His research uses modeling physical systems in terms of ordinary and partial differential equations. Detailed studies are obtained using functional analytic, asymptotic and perturbation analysis, and numerical computation. The over-arching goal of this research is to connect between the mathematical and physical aspects arising from these problems and make useful predictions about physical systems.

• Numerical Analysis
• Fluid Dynamics
• Applied Math
• Applications in Biology and Oceanography

Professor Kim is interested in interdisciplinary research problems at the interface between mathematics, science and engineering. In particular, he studies wave propagation in random media with applications to biomedical optics and wireless communications.

This research includes the study of differential and integral equations, asymptotic analysis, scientific computing and inverse problems.

Lower-dimensional topology and geometry

• Large-scale optimization
• Scientific computation and numerical analysis
• Compressed sensing and signal processing
• Computational biology
• Global optimization

Dr. Meza studies nonlinear optimization with an emphasis on methods for parallel computing. He has also worked on various scientific and engineering applications including scalable methods for nanoscience, power grid reliability, molecular conformation problems, optimal design of chemical vapor deposition furnaces, and semiconductor device modeling.

• Numerical solution of partial differential equation (PDEs) 
• Inverse problems
• Large-scale PDE-constrained optimization
• Uncertainty quantification

Professor Tokman's research is focused on building mathematical models of physical phenomena and developing efficient numerical methods for problems in science and engineering. In particular, she has been developing numerical techniques, which allow fast integration of large nonlinear systems of differential equations with widely varying temporal scales. Professor Tokman has worked on modeling large scale behavior of astrophysical and laboratory plasmas, including evolution of coronal loops in the solar atmosphere and plasma configurations arising in fusion related experiments. Her research interests also include computational biology, in particular, modeling experimental manipulations of biomolecular structure of living cells.