## 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 | |

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

Computational neuroscience; mathematical biology; machine learning; algorithms; distributed computing; graph theory; dynamical systems; high-dimensional probability and statistics | |

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. | |

My current research focuses on the following areas: 1. Statistical and algorithmic applications of random matrix theory, spin glass theory and integrability theory; 2. Mathematical and statistical foundation for manifold learning and machine learning; 3. Non-stationary time series analysis and functional time series analysis. [Related Courses] | |

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. | |

Mathematical Physics; Quantum Information [Related Courses] | |

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. | |

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. | |

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

My research interests are in Partial Differential Equations, specifically those
equations which arise from fluid dynamics. Within this vast field, I have thus
far concentrated on obtaining rigorous results related to the boundary layer
theory, which describes the behavior of a viscous fluid in the vicinity of a solid
wall at high Reynolds number. | |

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

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] | |

Mathematical physiology, neuroscience, cardiac electrophysiology. | |

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

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] | |

Hari Manikantan works on mathematical modeling of continuum mechanics, and is broadly interested in problems involving fluid dynamics, multiphase flows, elasticity, soft matter, numerical methods, rheology, biophysics, hydrodynamic stability, nonlinear dynamics, and pattern formation. His current research interests include the nonlinear rheology of fluid interfaces in lipid layers, emulsions, and foams; the configurational dynamics and stability of elastic microfilaments such as biopolymers; and the flow of non-Newtonian fluids in porous media with applications in plant vasculature. [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. | |

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] | |

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. | |

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] | |

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

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

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

Scientific computing, solid mechanics, fluid
mechanics, computer graphics | |

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] | |

Valdovinos studies the structure and dynamics of ecological networks at ecological and evolutionary scales; including their resilience to biodiversity loss, biological invasions, climate change, and exploitation by humans. Her main research lines include plant-pollinator systems and food-webs, which she studies using a combination of mathematical and computational approaches. [Related Courses] | |

I am a Professor in the departments of Mathematics and of Microbiology and Molecular Genetics at UC Davis. I am a mathematical biologist who specializes in the applications of topological methods and computational tools to the study of DNA packing, DNA-protein interactions, and DNA rearrangements. | |

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

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] |