Professors' Research Areas
- Professor Ablowitz’s work centers around nonlinear waves, integrable systems, and physical applied mathematics — e.g., nonlinear optics and water waves and applications of complex analysis.
- Professor Ablowitz’s work centers around nonlinear waves, integrable systems, and physical applied mathematics — e.g., nonlinear optics and water waves and applications of complex analysis.
- Professor Becker's investigates algorithms for signal processing and statistics, usually via optimization. Current focus includes compressive parameter extraction, randomized sketching for large data sets, computational imaging/super-resolution/phase-retrieval, and algorithms for semi-definite programming problems such as robust PCA formulations and SDP relaxations of bilinearly constrained problems. At ¶¶Òõ¶ÌÊÓƵ, he collaborates with groups in computer science, electrical engineering, mechanical engineering, and the (ICS).
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- Professor Becker's investigates algorithms for signal processing and statistics, usually via optimization. Current focus includes compressive parameter extraction, randomized sketching for large data sets, computational imaging/super-resolution/phase-retrieval, and algorithms for semi-definite programming problems such as robust PCA formulations and SDP relaxations of bilinearly constrained problems. At ¶¶Òõ¶ÌÊÓƵ, he collaborates with groups in computer science, electrical engineering, mechanical engineering, and the (ICS).
- Professor Beylkin's current research concentrates on numerical algorithms for multivariate functions with a wide range of applications, in particular in Quantum Chemistry. His research interests also include problems of wave propagation, inverse problems and signal processing, see /amath/gregory-beylkin-papers-preprints
- The primary research in Professor Bortz’s group is on mathematical biology, specifically bacterial community population dynamics and biomechanics, cellular migration, infectious diseases, and designs for an artificial pancreas. Bortz also has projects on information theoretic model selection, computational experimental design, and emergent numerical computations.
- Professor Dukic’s main research interests are in Bayesian modeling, inference, and computational statistics, with applications to a wide variety of fields, ranging from medicine and ecology to risk and insurance.
- Professor Dukic’s main research interests are in Bayesian modeling, inference, and computational statistics, with applications to a wide variety of fields, ranging from medicine and ecology to risk and insurance.
- Bengt Fornberg, Professor
- Professor Fornberg’s main research interests are in developing, analyzing, and implementing numerical methods, in particular for solving PDEs to high orders of accuracy. Such methods include pseudospectral and high accuracy finite difference methods and, in particular, methods based on radial basis functions (RBFs). The main application areas include computational fluid dynamics, geophysical and astrophysical flows, and seismic exploration.
- Professor Fornberg’s main research interests are in developing, analyzing, and implementing numerical methods, in particular for solving PDEs to high orders of accuracy. Such methods include pseudospectral and high accuracy finite difference methods and, in particular, methods based on radial basis functions (RBFs). The main application areas include computational fluid dynamics, geophysical and astrophysical flows, and seismic exploration.
- ​Ian Grooms, Assistant Professor
- Professor Grooms' research is focused on the development of multiscale analytical and computational models in support of climate, atmosphere, and ocean science. Professor Grooms’ current projects include the development of a data assimilation framework for superparameterization models (superparameterization is a multiscale computational method used primarily in global atmospheric modeling), and the development of stochastic models of energy and tracer transport by ocean mesoscale eddies.
- Professor Grooms' research is focused on the development of multiscale analytical and computational models in support of climate, atmosphere, and ocean science. Professor Grooms’ current projects include the development of a data assimilation framework for superparameterization models (superparameterization is a multiscale computational method used primarily in global atmospheric modeling), and the development of stochastic models of energy and tracer transport by ocean mesoscale eddies.
- Mark Hoefer, Professor
- Professor Hoefer’s research involves mathematics and experiments on superfluid-like dynamics of nonlinear, dispersive media. Fascinating properties of coherent wave structures such as dispersive shock waves and solitons are investigated with applications to magnetic materials, geophysical fluids (surface and internal ocean waves, magma migration), nonlinear optics, and Bose-Einstein condensates.
- Professor Hoefer’s research involves mathematics and experiments on superfluid-like dynamics of nonlinear, dispersive media. Fascinating properties of coherent wave structures such as dispersive shock waves and solitons are investigated with applications to magnetic materials, geophysical fluids (surface and internal ocean waves, magma migration), nonlinear optics, and Bose-Einstein condensates.
- Keith Julien, Professor
- Professor Julien’s primary area of research is focussed in the mathematical geo- and astro-physical sciences. Specifically, the modeling of dynamical processes, instabilities and turbulence occurring within the extreme parameter regimes typical of geophysical and astrophysical flows. Utilizing multiscale asymptotics, particular emphasis is placed on the identification of reduced PDE models that both accurately captures limiting solutions and describe key phenomena such as coherent structures, the transport and organization of large-scale flows, mean flow generation, and wave propagation Example areas include protoplanetary disks, stably and unstably stratified flows (such as penetrative convection, rotating and magneto- convection), shear flows and boundary effects in turbulent convection. Complimentary to these interest is the development of fast numerical algorithms for the purpose of numerical simulations on state of the art high performance computing architectures.
- Professor Julien’s primary area of research is focussed in the mathematical geo- and astro-physical sciences. Specifically, the modeling of dynamical processes, instabilities and turbulence occurring within the extreme parameter regimes typical of geophysical and astrophysical flows. Utilizing multiscale asymptotics, particular emphasis is placed on the identification of reduced PDE models that both accurately captures limiting solutions and describe key phenomena such as coherent structures, the transport and organization of large-scale flows, mean flow generation, and wave propagation Example areas include protoplanetary disks, stably and unstably stratified flows (such as penetrative convection, rotating and magneto- convection), shear flows and boundary effects in turbulent convection. Complimentary to these interest is the development of fast numerical algorithms for the purpose of numerical simulations on state of the art high performance computing architectures.
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- Professor Kleiber’s current research interests include statistical climatology, spatial statistics with particular emphasis on multivariate processes and computational challenges, calibration and emulation of complex geophysical computer experiments, statistics for energy applications and stochastic modeling of physical systems.
- Professor Kleiber’s current research interests include statistical climatology, spatial statistics with particular emphasis on multivariate processes and computational challenges, calibration and emulation of complex geophysical computer experiments, statistics for energy applications and stochastic modeling of physical systems.
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- Professor Lladser’s research interests are at the interface of applied and discrete probability and problems arising in computer science and computational biology, with an emphasis on discrete probability, analytic combinatorics, and asymptotic analysis. The overarching vision of his research is a synergism of mathematics and science.
- Professor Lladser’s research interests are at the interface of applied and discrete probability and problems arising in computer science and computational biology, with an emphasis on discrete probability, analytic combinatorics, and asymptotic analysis. The overarching vision of his research is a synergism of mathematics and science.
- Professor Meiss' specializes in dynamical systems theory for the study of Hamiltonian dynamics, the transition to chaos, and the theory of transport. Recent projects include the design of optimal mixers for passive scalars in laminar flows, the geometry of transport in volume preserving maps, the symplectic and Poisson structure of fluid dynamics, bifurcations and stability in four-dimensional symplectic maps, and the for fusion energy through a collaboration recently funded by the Simons Foundation.
- After receiving a PhD in 1980 in Physics from the University of California at Berkeley, he was a research scientist at the Institute for Fusion Studies from 1980-89. He joined the newly formed Department of Applied Mathematics in 1989. He is a Fellow of the American Physical Society, author of the textbooks Differential Dynamical Systems (SIAM, 2017) and, with R.D. Hazeltine, Plasma Confinement (Dover, 12003), and co-editor, with R.S. MacKay, of Hamiltonian Dynamical Systems: a Reprint Collection (Adam-Hilger, 1987).
- Professor Restrepo studies complex systems formed by many interacting units using techniques from Nonlinear Dynamics. His main area of research is the analysis of dynamical processes on complex networks, such as synchronization of coupled oscillators and propagation of excitation cascades. The goal of this research is to uncover the interplay between the structure of the network and the dynamics of these processes. He is also working on understanding how the heart can develop abnormal rhythms by constructing mathematical models of heart cell dynamics and analyzing their behavior.