## List of Faculty in the Graduate Group in Applied Mathematics (GGAM)

GGAM comprises faculty members from departments across the campus, including its home, the Department of Mathematics. Below is a brief description of faculty research, links to personal and departmental web pages plus some "Related Courses" which can serve as a general study guideline for students interested in research with a particular faculty member. Students who want a more complete description of a faculty member's research interests are encouraged to contact them.

Name | Research/Related Courses |
---|---|

Analytical, computational and experimental studies of turbulent flame propagation; diamond synthesis via chemical vapor disposition; combustion instabilities; development of algorithms for the computational study of reactive-flow dynamics | |

Computational and Mathematical Biology. Biophysical models of DNA. Topological Data Analysis (TDA) in genetics. Modeling of DNA under spatial confinement: design of viral particles for nanotechnological purposes and modeling of mitochondrial DNA in trypanosomes. Application of TDA to cancer genetics. [Related Courses] | |

Time series analysis, structural break analysis, theoretical/mathematical questions arising in
fields of application, such as economics, finance and environmental science.
[Related Courses] | |

Computational biology, mathematical modeling of
biological systems, statistical signal processing and inverse problems with applications to genomics and structural biology, machine learning. In particular, I am interested in using probabilistic models and statistical inference to predict RNA structural dynamics from biochemical structure probing data and biophysical principles. | |

Numerical linear algebra (theory, algorithm development & analysis) | |

Inferential and computational issues in non-parametric statistics, high-dimensional statistics, network analysis and stochastic optimization. [Related Courses] | |

Topology and Geometry of bimolecular structures, focusing on DNA. Structural transitions and their roles in regulation. | |

Multiscale asymptotics for PDEs; atmospheric science; fluid dynamics. [Related Courses] | |

Computer and information security, assurance, vulnerabilities analysis, design of secure systems and software, formal models of access control, network security, intrusion detection.
| |

Computational harmonic analysis; harmonic analysis on graphs and manifolds; numerical analysis. [Related Courses] | |

Time series, spatial analysis, model building, resampling methods, discrete data | |

Linear and nonlinear programming, global optimization, neural networks, control systems and manufacturing systems. | |

Characteristic based schemes; transonic flows; mesh generation. | |

Computational fluid dynamics; mathematical biofluid dynamics; mathematical models in biology. | |

Numerical modeling in Atmospheric Science. | |

Information science and technology in design and manufacturing, computational science, numerical analysis, multimedia, real-time computing, robotics. | |

Physics of computation, dynamical systems, statistical mechanics, structural complexity, evolutionary dynamics, machine learning, and distributed robotics. [Related Courses] | |

Network theory, statistical physics, computational science, probability, applied math, cellular automata, and networking protocols.
| |

Algorithm design for data mining and other areas of artificial intelligence. Applications to novel high impact areas of social importance. [Related Courses] | |

Discrete mathematics, algorithms in algebra and geometry. [Related Courses] | |

Computational and theoretical fluid dynamics and transport phenomena. Multiphase flows, inert and reactive; emerging materials processing methodologies; free surface and interfacial flows; microscale transport phenomena and fluidics; bioengineering applications. | |

Our lab is interested in neural mechanisms underlying higher-order brain functions linking perception and action, especially decision making. We are working on answering the question how the brain processes sensory information and combines it with other information in order to select what action to take next and when to take that action. So far, these mechanisms have mainly been studied from a psychological point of view, whereas neurophysiologists have largely concentrated on lower-level mechanisms. We are trying to bridge this gap by utilizing both behavioral and neurophysiological methods and by using mathematical models for exploring potential neural mechanisms. | |

Molecular computing, self-assembly, chemical reaction networks, distributed computing, theory of computing, algorithmic information theory, probability [Related Courses] | |

Process conrol, dynamics and design; computational modeling and simulation. | |

Simulation of soft-condensed matter by Monte Carlo or Molecular Dynamics simulation. Development of Advanced Simulation Techniques. | |

Network optimization, decision making under uncertainty, and civil infrastructure systems management, with an emphasis on applied mathematics. | |

Imaging, inverse problems, wave propagation, turbulent transport. | |

Geometrical algorithms and representations; computer-aided design and manufacturing; numerical analysis and scientific computing; particle simulation schemes (Coulomb systems); geometrical optics. | |

Numerical linear algebra; iterative solution of large linear systems; dimension reduction of large-scale systems; linear algebra problems in information retrieval; sparse matrix computations; numerical solution of partial differential equations; computational photonics; algorithms for VLSI circuit and device stimulation; numerical problems in control theory; structured matrices; interior-point methods, large-scale optimization problems; semidefinite programming. | |

Computational neuroscience | |

Probability; cellular automata. [Related Courses] | |

Numerical analysis and methods for molecular modeling, self-assembly in molecular ensembles, computational molecular and statistical mechanics, radiation damage in crystalline materials, vortex dynamics, perturbation techniques for nonlinear oscillators and soliton systems, Josephson systems, superconducting device physics, phase-locking. | |

Atmospheric sciences general circulation, dynamics, numerical modeling, observations. [Related Courses] | |

Linear and nonlinear systems; multi-input, multi-output feedback control systems; decentralized control design; robust and reliable control design. | |

Mathematical biology, mathematical modeling, Newtonian and non-Newtonian fluid dynamics, and numerical analysis. | |

Numerical methods of quantum mechanics; Large-scale parallel computing; Molecular dynamics. [Related Courses] | |

Mechanical Aerospace Engineering. Transonic aerodynamics, computational fluid dynamics; numerical solutions of partial differential equations. | |

Computert-aided geometric design (CAGD); Scientific Visualization and computer graphics; Grid/mesh generation (triangulation methods), computer vision (edge/feature detection), and robotics. [Related Courses] | |

Flow and transport processes in ground water and in the vadose zone; stochastic analysis of such processes in heterogeneous porous systems; numerical modeling; assessment and remediation of ground water contamination; nonpoint source pollution of ground water; geostatistics.
Check out this
site to view videos of a colloquium, Advanced Modeling Concepts for Environmental Sciences.
| |

Mathematics, topology, differential geometry, mathematical physics. | |

Environmental Studies and Mathematics. Theoretical population biology including mathematical ecology and mathematical genetics; qualitative theory of differential equations, differential delay equations, bifurcation theory. | |

Machine Learning, optimization, big
data analytics, parallel computing. [Related Courses] | |

Nonlinear wave propagation, continuum mechanics, singular perturbation methods, and nonlinear hyperbolic partial differential equations. | |

Experimental and computational cardiac dynamics; stability of calcium control system; origins of arrhythmias; optimal population variability. | |

Geodynamics (continuum mechanics applied to geologic problems). Computational fluid dynamics; models of convection in the Earth's mantle and viscoelastic deformation in the Earth's crust.
http://geodynamics.org/ [Related Courses] | |

My research program focus on understanding protein structures. I am interested in characterizing their shapes using mathematical and computational approaches, and to use this information to improve our understanding of their stability. I am also interested in characterizing the subset of sequence space compatible with a protein structure: this is an indirect approach to understanding protein sequence evolution. In parallel, I am involved in the development of new algorithms for predicting the structure of a protein,
based on its sequence. My department web pages are:
http://www.cs.ucdavis.edu/people/faculty/koehl.html
in CS and
http://genomecenter.ucdavis.edu/koehl_cv.html
at the Genome Center. | |

Mathematical optimization, in particular integer
programming and mixed-integer programming; computational discrete
mathematics [Related Courses] | |

Study of hydrodynamics and dispersion in coastal ocean, including bays, estuaries and nearshore. Dispersion problems related to environmental issues, e.g., water quality, population ecology, algal blooms, estuarine habitat. Hydrodynamic problems include stratified flow, surface wind forcing, flow-topography interactions (e.g., jets, wakes, boundary layers), and waves/tides/internal waves. [Related Courses] | |

Mulitdimensional signal processing, statistical signal processing inverse problems, estimation and stochastic processes, linear systems theory, scientific computation. [Related Courses] | |

Mathematical physiology, neuroscience, cardiac electrophysiology. | |

Methods and theory in high-dimensional statistics, robust statistical learning, network data analysis, and signal processing.
[Related Courses] | |

Environmental and natural resource economics, energy economics, industrial organization, game theory, optimal control theory, structural econometric estimation of dynamic optimization problems, structural econometric estimation of static and dynamic games, spatial analysis. | |

Network resource management, optimization, machine learning. [Related Courses] | |

My main research areas are in high-dimensional statistics and machine learning, with a particular focus on bootstrap methods and randomized numerical linear algebra. [Related Courses] | |

Operations research and numerical optimization [Related Courses] | |

My research interests include the development of numerical
methods for the solution of complex problems in engineering and science,
mostly at the continuum scale; Complex rheology: multiscale and
continuum methods for incompressible viscoelastic flows; Multiphase
flows: compressible and incompressible flows of fluids and
elastic-plastic solids in time-dependent domains, interfacial processes;
Constitutive modeling: equations of state, thermodynamic modeling,
symmetry invariants; and Charged systems: plasma physics, boundary
charge and bilayer problems.
[Related Courses] | |

Markov chain Monte Carlo, random walks on graphs, randomized algorithms, probability on trees. | |

Functional Data Analysis, Semiparametric Modelling, Applications in Biodemography, Genetics, Medicine, e-Commerce and Finance. [Related Courses] | |

Mathematics. Algebra, geometry, global analysis and mathematical physics. | |

Mathematical physics; statistical mechanics; quantum spin systems; rigorous results in quantum mechanics and condensed matter physics; quantum information and computation. [Related Courses] | |

Numerical and asymptotic methods applied to problems in atmospheric dynamics and geophysical fluid dynamics. | |

My research interest is parallel computing; our work
primarily concentrates on the graphics processor (GPU) as a
general-purpose, highly-parallel processor. We have extensive experience
with both parallel algorithms and data structures as well as
applications that benefit from parallel approaches.
[Related Courses] | |

Non-Newtonian fluid mechanics; suspension mechanics. [Related Courses] | |

Fluid and suspension mechanics and rheology.
| |

Numerical solutions of PDEs, thermodynamics, droplets, geophysics, mantle convection. | |

Theoretical computer science. Foundations of data science. Matrix computations. Machine learning. Convex geometry. Optimization. [Related Courses] | |

Robust statistics, computational statistics, game theory, quality control. | |

Cryptography, including definitions, models, reductions, and proofs. Practice-oriented provable-security. [Related Courses] | |

Combinatorics, probability, experimental mathematics, number theory, geometry. [Related Courses] | |

Computational science & engineering; complex multiscale systems; driven threshold systems, including earthquakes and neural networks; statistical physics. | |

Applied and computational harmonic analysis, statistical signal processing, image analysis, feature extraction, pattern recognition, potential theory,elliptic eigenvalue problems, geophysical inverse problems, human and machine perception. [Related Courses] | |

Environmental and natural resource economics, mathematical ecology and epidemiology, optimal control theory, spatial and dynamic analysis of economic-ecological models, bioeconomic analysis, panel data econometric estimation. | |

Function, Design, and Evolution of Cellular and Molecular Networks [Related Courses] | |

Microeconomic Theory, Game Theory, Experimental Economics, Industrial Organization, Bounded Rationality [Related Courses] | |

Applications of dynamical systems and stochastic processes to ecology, epidemiology, and evolution. [Related Courses] | |

I work in quantum field theory and string theory applying methods of modern mathematics, especially topology, noncommutative geometry and arithmetic geometry. [Related Courses] | |

Machine learning, network science, high-dimensional statistics [Related Courses] | |

Hyperbolic PDE, moving free-boundary and interface problems,
mathematical fluid dynamics [Related Courses] | |

[Related Courses] | |

Random matrix theory; probability theory; mathematical physics; combinatorics. [Related Courses] | |

Numerical analysis, applied harmonic analysis, digital signal processing, approximation theory, scientific computing. [Related Courses] | |

Computational mechanics, fracture, finite element and meshfree methods,
maximum-entropy approximations, partition-of-unity finite element methods
in quantum mechanics, numerical analysis of PDEs [Related Courses] | |

Shock waves, general relativity, applied analysis. [Related Courses] | |

Partial differential equations, nonlinear elasticity, Newtonian and non-Newtonian fluid dynamics, mechanics of deformable solids. [Related Courses] | |

Mathematical physics; statistical mechanics, the theory of exactly solvable models, completely integrable systems. [Related Courses] | |

research is in experimental physics and cosmology, which
includes development of new astronomical surveys, new detectors,
astronomical instrumentation and analysis algorithms -- aimed at
unraveling the nature of dark energy and dark matter. I have developed
cameras and analysis techniques for imaging of the distant, younger
universe. [Related Courses] | |

My research focuses largely on the design and evaluation of
innovative modeling techniques that improve the accuracy and eciency of
atmospheric general circulation models, and using these models to
answer scientic questions related to atmospheric dynamics and the
interplay of dynamics on regional and global scales. [Related Courses] | |

Artificial neural networks, artificial life; simulation and modeling, computer architecture; optimization, genetic algorithms. [Related Courses] | |

My research interest is primarily based in mathematical biology. In particular, I am interested in using mathematical models to predict macroscopic biological function from single molecule mechanics (mechanobiology). Topics of recent interest are muscle contraction and the response of cells to mechanical stimuli. This research benefits greatly from extensive experimental collaborations.
[Related Courses] | |

Dimension reduction methods; functional data analysis; longitudinal data analysis; nonparametric functional estimation; aging research; survival analysis. [Related Courses] | |

Stochastic optimization, approximation theory for optimization problems, nonsmooth analysis. | |

Heuristic search optimization techniques. Production and supply chain planning. Robust multivariate data analysis.
Stochastic Programming (integer). Bioinformatics. [Related Courses] | |

Geometric measure theory and its application; optimal mass transport problems; mathematical biology; geometric variational problems in singular spaces. | |

Vehicular traffic flow, network optimization and control of transportation systems.
[Related Courses] |