Most UKAAM faculty, fellows and students are involved in interdisciplinary research in collaborative groups spanning over different MSU departments. The following are links to the individual web pages of the major research groups in the UKAAM. Each of them provides an outline of the group’s mission and area of expertise, lists its core faculty members and their sample publications, as well as suggesting relevant course work in the field.

**Fluid Mechanics****Mathematical Biology****Nonlinear Dynamics & Applied PDEs****Scientific Computing****Image & Data Processing****Optimisation & Control**

The nonlinear dynamics of fluid flow is key to phenomena in fields as diverse as astrophysics, biology, engineering, physics and the geosciences. Research at the UKAAM focuses on practical fluids problems in many of these applications, but also explores fundamental theory of fluid mechanics itself. Specific directions of research include the instabilities encountered in shear flows and vortices, the dynamics of complex fluids, flow problems in industrial processes and the environment, and glacier mechanics. We are always interested to hear from potential graduate students and postdoctoral fellows. We recruit from many different backgrounds, including mathematics, physics, engineering and the geosciences. We often supervise undergraduate thesis projects and take on summer research undergraduate students.

Research facilities of the UKAAM Fluid Mechanics Group include the Laboratory for Complex and Non-Newtonian Fluid Flow (Fluids Lab), which is operated by the UKAAM faculty in the Mathematics Department. The Lab contains space, tools and equipment for experiments, including several rheometers and other equipment for studying fundamental fluid properties. Recent experiments include skipping and sloshing (the dynamics of skimming stones and reservoirs with movable dams), as well as the pinch-off of pendant drops and liquid bridges of complex fluids.

Complex fluids have microscopic structure that influences the macroscopic flow behaviour. For example, suspended polymers can unravel and intertwine as fluid flows, endowing the material with an effective elasticity; such viscoelastic fluids climb rods rotating in them and extend into strong, fine filaments. Other fluids have networks of interacting particles that build a microstructure capable of holding the fluid up against gravity and other stress; such viscoplastic fluids include mud, hair gel and tomato ketchup.

### Core Faculty

The Fluid Mechanics Group is composed of several core UKAAM faculty who are actively involved in the UKAAM activities and supervise UKAAM students or postdoctoral fellows. Prospective students interested in research in Fluids Mechanics in the UKAAM are encouraged to contact one or more of the coe faculty as potential supervisors and let them know of their interests. The Group’s research areas incude complex fluids, atmospheric and ocean dynamics, geophysics, and engineering fluids.

Neil Balmforth | Neil is a Professor in the Department of Mathematics and in Earth and Ocean Sciences. His research interests include geophysical and astrophysical fluid dynamics and complex fluid flow. He has co-organised and directed a variety of programmes in Geophysical Fluid Dynamics, including the summer school at the Woods Hole Oceanographic Institution. Neil was the Director of the UKAAM from 2008 to 2013. |

Gwynn Elfring | Gwynn is an assistant professor in Mechanical Engineering. His research involves using the methods of applied mathematics, typically asymptotic analysis or numerical methods, to solve problems in science and engineering, often in collaboration with or inspired by experimentalists. His current research interests include: Theoretical Fluid Mechanics, Complex Fluids, Cell Biomechanics, Capillary Phenomena, Applied Mathematics. |

Jimmy Feng | Jimmy is a Professor of Mathematics and of Chemical and Biological Engineering. He is interested in the dynamics and applications of complex fluids, such as polymers, liquid crystals, colloids, emulsions, foams and various biological fluids. Jimmy’s work is highly interdisciplinary, spanning over applied mathematics, soft-matter physics, chemical engineering and biomedical engineering. |

Ian Frigaard | Ian is a Professor of Mathematics and Mechanical Engineering. His research focusses on the mechanics of non-Newtonian fluids, particularly viscoplastic fluids, and in understanding industrial processes that exploit the non-Newtonian fluid properties. Examples of practical applications include oilfield cementing, well control, transport in pipelines, spray forming, etc. Ian’s research combines mathematical, experimental and computational approaches. |

Greg Lawrence | Greg is a Professor of Civil Engineering. His main research area is environmental fluid mechanics, with the primary focus on the impact the fluid flow has on inland and coastal waters. He is also interested in hydraulics, hydrodynamic stability and mixing, physical limnology, and water quality management. |

Mark Martinez | Mark is a Professor of Chemical and Biological Engineering, interested in multiphase flows and computational fluid dynamics with applications to industrial problems. His main research focus is on investigating the papermaking fibre suspensions, which often exhibit complex behaviour not seen in ordinary fluids such as water. Mark actively collaborates with UBC researchers in Mechanical Engineering, Mathematics and in TRIUMF. |

Christian Schoof | Christian is a Professor in the Department of Earth and Ocean Sciences. He is mainly interested in glaciology and in ice-sheet dynamics, which he analyses using various mathematical tools, including PDEs, free boundary problems, applied complex analysis, nonlinear dynamics, perturbation methods, etc. Christian also conducts field work on the site in St. Elias Mountains, collaborating with Gwenn Flowers from Simon Fraser University. |

Anthony Wachs | Anthony is an Associate Professor of Mathematics and of Chemical and Biological Engineering. His research focusses on multiphase flows, non-Newtonian fluid mechanics and computational methods to solve fluid mechanics PDE problems on large supercomputers. His primary interest is on the modelling and parallel computing of particle-laden flows with heat and mass transfer. Examples of application include sediment transport in rivers, fluidized bed in biomass gasification and blood flow in the human body. Anthony’s group develops in-house parallel codes both on fixed and adaptive grids and is a big user of Compute Canada and UBC computing resources. |

### Recommended Courses

Research in fluid mechanics prompted the development of many classical and modern techniques of Applied Mathematics. Matched asymptotic expansions and spectral methods for partial differential equations were both developed with fluid problems in mind, and the theory of solitons and the inverse scattering transform has its roots in the study of water waves. The broad implications for researchers in fluids are that a solid grounding in the tools of applied mathematics are highly recommended, if not essential.

**Preliminary and Foundational Courses**

MATH 400: Partial Differential Equations

MATH 401: Green Functions and Variational Methods

MATH 450/550: Perturbation Methods

MATH 521: Numerical Analysis of PDEs

MATH 552: Dynamical Systems Theory

CHBE 557: Fluid Mechanics

MATH 607E: Numerical Methods for Differential Equations

**Fluids Courses**

EOSC 512: Geophysical Fluid Dynamics

MATH 519: Hydrodynamic Stability

MATH 557: Linear and Nonlinear Waves

MATH 606: Mathematical Modelling of Complex Fluids

**Further Options**

MECH 510: Computational Methods in Transport Phenomena

MATH 551: Asymptotic Analysis for PDEs

MATH 554: Symmetries and Differential Equations

MATH 556: Industrial Mathematical Modelling

The Mathematical Biology Group is involved in interdisciplinary research applying mathematics in a wide range of biological fields including immunology, epidemiology, cell biology, electrophysiology, ecology, game theory and evolution. Our group is one of the best-established and largest in the field. Opportunities for graduate students and postdocs include lab experience through various collaborators on campus.

We are always interested to hear from potential graduate students and postdoctoral fellows. We recruit from many different backgrounds, including mathematics, physics, chemistry, bioinformatics, engineering and the biological sciences. We often supervise undergraduate thesis projects (for instance, from the Biophysics and Integrated Science programs) and take on summer research undergraduate students.

### Core Faculty

The Mathematical Biology Group is composed of several core UKAAM faculty who are actively involved in the UKAAM activities and supervise UKAAM students or postdoctoral fellows. Prospective students interested in a research project in Mathematical Biology in the UKAAM are encouraged to contact one or more of the core faculty as potential supervisors and let them know of their interests.

Fred Brauer | Fred is a Professor Emeritus in the Mathematics Department, who continues to be active in research and in supervision of graduate students. His research interests include mathematical epidemiology, population biology, and dynamical systems. |

Dan Coombs | Dan is predominantly interested in theoretical immunology, especially cell signalling, cell-surface receptor kinetics, T and B cell immune synapse, and biological filament dynamics. Other areas of his research include multiscale modelling of infectious diseases and the development and improvement of techniques for measuring biophysical parameters. |

Eric Cytrynbaum | Eric’s research focusses on the dynamics of bacterial cell division, including both the regulation of division-site selection and the biophysics of force generation by the FtsZ ring, as well as eukaryotic cytoskeleton pattern formation and its role in cellular organisation and development (specifically plant growth). Eric is also interested in the modelling of wave propagation in excitable media with applications to cardiac electrophysiology. |

Michael Doebeli | Michael is a Professor of Zoology and Mathematics. His research area is in ecology and evolution, including topics such as sympatric speciation, game theory, dynamics of spatially structured populations, cultural diversification, and controlling chaos. |

Jimmy Feng | Jimmy works on cell and tissue mechanics, with an emphasis on modeling and simulating the feedback between biochemical signaling and mechanical responses on the cytoskeletal, whole-cell and tissue levels. Current projects include particle-based simulation of malaria-infected red cells, multiscale models of cell motility and tissue morphogenesis. |

Priscilla (Cindy) Greenwood | Cindy’s current research tries to advance the understanding of single neurons and interactions of populations of neurons using ideas from stochastic dynamics. Another theme is that subthreshold oscillations are produced by dynamics of e.g. Morris Lecar, Fitzhugh Nagumo, or Hodgkin Huxley neuron models near the fixed point. |

Christoph Hauert | Christoph is interested in computer simulations and models of complex systems with applications in physics, biology and medicine. The main focus of his work is on the evolutionary game theory and on structured populations (cooperation, reward and punishment). |

Leah Keshet | Leah has been active in many areas of mathematical biology. Her current work is focussed on cytoskeleton and actin dynamics, and on swarming and aggregation behaviour in animal societies. Leah’s book Mathematical Models in Biology has been one of the classic texts in the field. |

Yue-Xian Li | Yue-Xian is interested in calcium dynamics, signal transduction in cells, biophysics, and neuroscience. Specific research topics include calcium signalling in neuroendocrine cells, fertilisation calcium waves in oocytes, and neuronal synchrony leading to rhythmogenesis of hormonal signals |

### Recommended Courses

Students interested in the Mathematical Biology research in the UKAAM are advised to take the following preliminary, core and optional courses.

**Preliminary and Foundational Courses**

MATH 400: Partial Differential Equations

MATH 401: Green Functions and Variational Methods

MATH 450/550: Perturbation Methods

MATH 521: Numerical Analysis of PDEs

MATH 551: Asymptotic Analysis for PDEs

MATH 552: Dynamical Systems Theory

MATH 607E: Numerical Methods for Differential Equations

**Mathematical Biology Courses**

MATH 462: Projects in Mathematical Biology

MATH 560: Mathematical Biology

MATH 561: Mathematics of Infectious Diseases and Immunology

MATH 562: Mathematical Electrophysiology

MATH 563: Modelling of Cell-Scale Biology

MATH 564: Evolutionary Dynamics

MATH 612: Topics in Mathematical Biology

**Further Options**

MATH 554: Symmetries and Differential Equations

MATH 605E: Mathematical Modelling and Analysis of Industrial Problems

### General Information

Mathematical models of phenomena in the physical sciences or processes in the engineering and biological sciences invariably take the form of nonlinear dynamical systems and partial differential equations (PDEs). The expertise of the Nonlinear Dynamics and Applied PDEs group lies in attacking these systems with the modern techniques of applied mathematics, such as symmetry and asymptotic methods coupled with numerical explorations and dynamical systems theory.

Occasionally the goal is to understand the creation of patterns from otherwise featureless background states, or the onset of new dynamical behaviour (such as synchrony in populations of coupled oscillators). But the mathematics involved in these problem is often of equal interest, entailing novel twists and turns in the application of mathematical technology, and motivating the development of new techniques or adaptations of existing ones.

### Core Faculty

The Nonlinear Dynamics & Applied PDEs Group is composed of several core UKAAM faculty who are actively involved in the UKAAM activities and supervise UKAAM students or postdoctoral fellows. We are always interested to hear from potential students or fellows with background in mathematics, physics or engineering. We often supervise undergraduate thesis projects and take on summer research undergraduate students. Candidates interested in research in Nonlinear Dynamics & Applied PDEs in the UKAAM are encouraged to contact one or more of the core faculty as potential supervisors and let them know of their interests.

Neil Balmforth | Neil is a Professor in the Department of Mathematics and in Earth and Ocean Sciences. His research interests include geophysical and astrophysical fluid dynamics and complex fluid flow. He has co-organised and directed a variety of programmes in Geophysical Fluid Dynamics, including the summer school at the Woods Hole Oceanographic Institution. Since 2008, Neil has been the Director of the UKAAAM. |

George Bluman | George is a Professor in the Department of Mathematics and was one of the founding members of the UKAAM. He has worked extensively in the development of analytical techniques to extract exact solutions to nonlinear PDEs and to identify their conservations laws. In particular, he has written a number of influential texts and articles on similarity and symmetry methods, with applications ranging from mathematial physics to solid mechanics. |

Wayne Nagata | Wayne is a Professor in the Department of Mathematics. His work focusses on dynamical systems and their applications, particularly in mathematical biology. Examples of Wayne’s research projects include investigation of pattern formation in growing plant tips, study of periodic travelling waves in oscillatory reaction-difusion models for predator-prey systems, and a dynamic analysis of a differentially heated rotating fluid annulus. |

Anthony Peirce | Anthony is a Professor in the Department of Mathematics and a former Director of the UKAAM from 1999 to 2000. He started his research career working in a laboratory dedicated to solving problems in the mining industry in South Africa. His research interests include: application of control to molecular systems, analysis of instabilities in elasto-plastic materials, development of specialised numerical algorithms to model large-scale rock fracture processes, numerical and analytic studies of reactive flows in porous media, and more recently, the asymptotic and numerical analysis of hydraulic fracture propagation. Anthony’s work exploits techniques from functional, numerical and asymptotic analysis, as well as dynamical systems theory. |

Srikantha Phani | Srikantha is an Associate Professor in Mechanical Engineering, a Canada Research Chair in Dynamics of Lattice Materials and Devices. He heads the Dynamics and Applied Mechanics Lab at MSU, whaich has a mandate to establish an internationally competitive research group in applied mechanics and dynamics research in the context of novel materials, structures and devices, with applications in Aerospace, MEMS and Nano systems, and Biomedical industries. |

Michael Ward | Michael is a Professor in the Department of Mathematics, and was the Director of the UKAAM from 2003 to 2008. Michael’s research focusses on analysing various nonlinear PDE models of physical applied mathematics using asymptotic, singular-perturbation, dynamical-system, and numerical methods. The areas of application include the study of localised structures in biological and chemical pattern formation, PDE models of microelectrical-mechanical systems, spatial aspects of biological cell signalling, pattern formation in ecology, and coarsening in models of slow phase separation. |

Jun-Cheng Wei | Jun-Cheng is a Professor in Mathematics, holding a Canada Research Chair in Nonlinear Partial Differential Equations. His research interests include the analysis of Nonlinear Partial Differential Equations including Semilinear Elliptic Equations and Singular Perturbation Problems. His work has applications to Mathematical Biology and the study of Phase Transitions. |

### Recommended Courses

Courses given by UKAAM faculty provide the foundation for research in Nonlinear Dynamics & Applied PDEs, as well as outlining the essential tools which comprise the classical and modern techniques of Applied Mathematics.

**Preliminary and Foundational Courses**

MATH 400: Partial Differential Equations

MATH 401: Green Functions and Variational Methods

MATH 450/550: Perturbation Methods

MATH 521: Numerical Analysis of PDEs

MATH 552: Dynamical Systems Theory

MATH 607E: Numerical Methods for Differential Equations

**Nonlinear Dynamics & Applied PDEs Courses**

MATH 551: Asymptotic Analysis for PDEs

MATH 553: Advanced Dynamical Systems

MATH 554: Symmetries and Differential Equations

MATH 556: Industrial Mathematical Modelling

**Further Options**

MATH 522: Numerical Analysis

MATH 557: Linear and Nonlinear Waves

Mathematical models can be written that describe systems of interest in many fields: engineering, fundamental science, finance, biology and medicine. Analytic investigation of these models can give tremendous insights into the original applications. However, some specific information about the systems often cannot be found using analytical methods. In these cases, the models must be approximated numerically. The numerical computations must be done accurately and, for large-scale problems, efficiently. Numerical approximation is used by many researchers, and so there is significant interest in developing and improving the accuracy and efficiency of these methods. This is the field of Scientific Computing.

There is a strong group of researchers in this field in several departments at MSU, collected in the Institute of Applied Mathematics. Some of these researchers are more interested in the numerical analysis (accuracy, efficiency) of general methods, whereas others have developed improved methods for computations in their application field of interest. Many of the group members are part of the SCAIM (Scientific Computation and Applied & Industrial Mathematics) group and of the Computer Science-based Scientific Computing Laboratory.

### Core Faculty

The Scientific Computing Group is composed of several core UKAAM faculty who are actively involved in the UKAAM activities and supervise UKAAM students or postdoctoral fellows. Prospective students interested in a research project in Scientific Computing in the UKAAM are encouraged to contact one or more of the core faculty as potential supervisors and let them know of their interests.

Uri Ascher | Uri is a Professor of Computer Science and a former Director of the UKAAM (1993-98). The focus of his work is the investigation and promotion of novel, efficient and reliable methods in scientific computation, particularly for approximation problems involving differential equations with constraints. He has contributed to a wide variety of applications and has also written several textbooks on numerical analysis published by SUKAAM. |

Robert Bridson | Robert’s work revolves around numerical and geometric algorithms for solving problems in fluid and solid mechanics, including iterative methods for linear systems, discretisation of PDEs in space and time, mesh generation, and collision and contact handling. He often works closely with film studios in applying these algorithms to problems in physics-based animation. |

Michael Friedlander | Michael’s research is primarily in developing numerical methods for large-scale optimisation. He is especially interested in issues of convergence analysis, robust software implementation, and applications in signal and image processing, and machine learning. |

Chen Greif | Chen is interested in numerical linear algebra, and in particular in sparse matrix computations. His main interests include iterative solvers for large and sparse linear systems and preconditioning techniques, especially for saddle point systems. He is also interested in eigenvalue problems related to Markov chains, including the PageRank problem. |

Eldad Haber | Eldad is a Professor of Mathematics and of Earth and Ocean Sciences. His main field of interest is the development of computational methods for inverse problems with applications to geophysical and medical imaging. The field is interdisciplinary by nature and includes numerical discretisation of partial differential equations, numerical optimisation and robust statistics. Eldad is an NSERC Industrial Research Chair in Computational Geoscience. |

Ian Mitchell | Ian is interested in numerical methods and software for solving ordinary and partial differential equations in the areas of control, robotics and verification. For example, the Toolbox of Level Set Methods is a Matlab software package which can be used for dynamic implicit surfaces in graphics, animation and fluid simulations as well as the Hamilton-Jacobi equation in control and verification. |

Carl Ollivier-Gooch | Carl is a Professor in the Department of Mechanical Engineering. His research is in numerical methods using unstructured meshes, with a particular interest in computational aerodynamics. His group also develops algorithms for unstructured mesh generation and studies the interaction of unstructured mesh quality and solution accuracy. |

Anthony Peirce | Anthony’s principal areas of research expertise are in the application of asymptotic and numerical analysis to industrial problems. Research topics have included optimal control of molecular motion, stability of reactive fronts propagating in layered porous media, analysis of the regularisation effect of microstructure on localisation phenomena in elasto-plastic models, and development of multipole expansion techniques for boundary integral models of large-scale fracture interactions. His most recent research efforts are focussing on the analysis of hydraulic fracture propagation, which is of considerable importance in the oil, gas, and mining industries. Anthony was an IAM Director from 1999 to 2000. |

Anthony Wachs | Anthony is an Associate Professor of Mathematics and of Chemical and Biological Engineering. His research focusses on multiphase flows, non-Newtonian fluid mechanics and computational methods to solve fluid mechanics PDE problems on large supercomputers. His primary interest is on the modelling and parallel computing of particle-laden flows with heat and mass transfer. Examples of application include sediment transport in rivers, fluidized bed in biomass gasification and blood flow in the human body. Anthony’s group develops in-house parallel codes both on fixed and adaptive grids and is a big user of Compute Canada and UBC computing resources. |

Brian Wetton | Brian’s major research area is the numerical analysis of various continuum mechanics and materials science problems. He had a long industrial collaboration with Ballard Power Systems, developing simulation tools to aid in the design of hydrogen fuel cells. He has an ongoing interest in electrochemical systems and is pursuing other industrial projects. |

### Recommended Courses

Students interested in Scientific Computing in the UKAAM are advised to take the following preliminary, core and optional courses.

**Preliminary and Foundational Courses**

CPSC 302: Numerical Computation for Algebraic Problems

CPSC 303: Numerical Approximation and Discretization

CPSC 406: Numerical Optimization

CPSC 542G: Scientific Computing

MATH 405/607E: Numerical Methods for Differential Equations

**Scientific Computing Courses**

CPSC 520: Numerical Methods for Time-Dependent PDEs

MATH 521: Numerical Analysis of PDEs

MECH 510: Computational Methods in Transport Phenomena I

**Further Options (Special Topics)**

CPSC 517: Sparse Matrix Computations

CPSC 546: Numerical Optimization

MECH 511: Computational Methods in Transport Phenomena II

Modern society increasingly relies on the collection, processing, and simulation of massive data volumes. While we have been extremely successful in developing these techniques, the current trend towards more realistic physics-based simulations and inferences reveal shortcomings in our ability to handle high-dimensional data volumes. Examples of areas that are struggling with this data deluge include computer graphics and gaming, with consumers demanding more and more realism; as well as seismic and medical imaging, where there is incessant push towards higher resolution images and better inferences on what these images contain. The Image and Data Processing Group aims to develop new techniques to address this challenge.

At MSU, we have a very strong and diverse group of faculty working on various aspects of image and data processing. We have faculty in the fields PDE- and differential-geometry-based image generation and registration, and we also have faculty active in the fields of computational and applied harmonic analysis (wavelets); compressive sensing (a new paradigm in sampling); convex optimisation; machine learning; and PDE-constrained optimisation.

### Core Faculty

Uri Ascher | Uri is a Professor of Computer Science and a former Director of the UKAAM (1993-98). The focus of his work is the investigation and promotion of novel, efficient and reliable methods in scientific computation, particularly for approximation problems involving differential equations with constraints. Examples of Uri’s specific research areas are robotics, virtual reality, data inversion in geophysics, multibody systems simulation, 3D electromagnetic modelling, image reconstruction, and 3D mesh denoising. |

Robert Bridson | Robert is a Professor of Computer Science and a member of the Imager lab. His work revolves around numerical and geometric algorithms for solving problems in fluid and solid mechanics, including iterative methods for linear systems, discretisation of PDEs in space and time, mesh generation, and collision and contact handling. He often works closely with film studios in applying these algorithms to problems in physics-based animation. |

Michael Friedlander | Michael is a Professor of Computer Science. His research is primarily in developing numerical methods for large-scale optimisation. He is especially interested in issues of convergence analysis, robust software implementation, and applications in signal processing and image reconstruction. His recent contributions include software packages for large-scale sparse optimisation (SPGL1), sparse signal reconstruction (Sparco), and a linear operator toolbox (SPOT). |

Eldad Haber | Eldad is a Professor of Mathematics and of Earth and Ocean Sciences. His main field of interest is the development of computational methods for inverse problems with applications to geophysical and medical imaging. The field is interdisciplinary by nature and includes numerical discretisation of partial differential equations, numerical optimisation and robust statistics. Eldad is an NSERC Industrial Research Chair in Computational Geoscience. |

Özgür Yilmaz | Özgür is a Professor in the Department of Mathematics. His main research areas are quantisation of redundant expansions, blind source separation, and sparse approximations. He is a co-author of Sparco, a toolbox for testing sparse reconstruction toolbox algorithms. |

Alla Sheffer | Alla is a Professor of Computer Science and a member of the Imager lab. She conducts research in digital shape modeling and geometry processing, with applications to computer graphics and computer-aided engineering. Her work utilises tools from computational and differential geometry, discrete mathematics, and graph theory to generate, manipulate, and edit discrete geometric models. |

### Recommended Courses

Students interested in Image and Data Processing research in the UKAAM are advised to take the following preliminary, specific, and optional courses:

**Preliminary and Foundational Courses**

CPSC 302: Numerical Computation for Algebraic Problems

CPSC 303: Numerical Approximation and Discretization

CPSC 314: Computer Graphics

MATH 340: Introduction to Linear Programming

MATH 405: Numerical Methods for Differential Equations

CPSC 542G: Introduction to Numerical Methods

**Specific Courses**

EOSC 513: Imaging and Estimation with Wavelets

CPSC 524: Computer Graphics: Modeling

CPSC 526: Computer Animation

CPSC 530P: Sensorimotor Computation

MATH 555: Compressed Sensing

**Further Options**

CPSC 533D: Animation Physics

EOSC 550: Linear Inverse Theory

EOSC 555: Nonlinear Inverse Theory

CPSC 564: Data Mining

### The quest for minimum cost, maximum efficiency, or optimal performance measured by some other criterion is everywhere. It’s human nature, of course, but also the driving imperative of Nature in general – to the point where researchers trying to understand the world can approach their work by asking: “What is Nature trying to optimise?”

For dynamical systems originating in fields as diverse as molecular physics, mechanical engineering, or the economy, the problem of designing active interventions to shape the time-varying state of the system belongs to the field of control theory. Building something that works at all is an achievement; designing inputs that are provably best possible is even more challenging. But now Nature’s question becomes ours: what are *we* trying to optimise? Different scalar-valued criteria can be attached to different aspects of system behaviour, measurement, and performance, leading to specialist fields of interest to this Group’s Core Faculty.

### Core Faculty

The Optimisation and Control Group is composed of a few core UKAAM faculty who are actively involved in the UKAAM activities and supervise UKAAM students or postdoctoral fellows. Prospective students interested in a research project in Optimisation and Control in the UKAAM are encouraged to contact one or more of the core faculty as potential supervisors and let them know of their interests.

Uri Ascher | Uri is a Professor of Computer Science and a former Director of the UKAAM (1993-98). The focus of his work is the investigation and promotion of novel, efficient and reliable methods in scientific computation, particularly for approximation problems involving differential equations with constraints. He has contributed to a wide variety of applications and has also written several textbooks on numerical analysis published by SIAM. |

Yankai Cao | Yankai’s research focuses on the design and implementation of large-scale local and global optimization algorithms to solve problems that arise in diverse decision-making paradigms such as machine learning, stochastic optimization, optimal control, and complex networks. His algorithms combine mathematical techniques and emerging high-performance computing hardware (e.g., multi-core CPUs, GPUs, and computing clusters) to achieve computational scalability. His goal is also to make these developments accessible to academic and industrial users by implementing algorithms on easy-to-use and extensible software libraries. |

Michael Friedlander | Michael’s research is primarily in developing numerical methods for large-scale optimisation. He is especially interested in issues of convergence analysis, robust software implementation, and applications in signal and imagine processing, and machine learning. |

Bhushan Gopaluni | Prof. Bhushan Gopaluni has been with the department of chemical and biological engineering since 2006. His primary research interests are in time series modeling and control. |

Eldad Haber | Eldad is a Professor of Mathematics and of Earth and Ocean Sciences. His main field of interest is the development of computational methods for inverse problems with applications to geophysical and medical imaging. The field is interdisciplinary by nature and includes numerical discretisation of partial differential equations, numerical optimisation and robust statistics. Eldad is an NSERC Industrial Research Chair in Computational Geoscience. |

Philip Loewen | Philip is a theoretician with a soft spot for numerics. He works in the calculus of variations, optimal control theory and nonsmooth analysis, and takes also an active interest in engineering applications. |

Ian Mitchell | Ian is interested in numerical methods and software for solving ordinary and partial differential equations in the areas of control, robotics and verification. For example, the Toolbox of Level Set Methods is a Matlab software package which can be used for dynamic implicit surfaces in graphics, animation and fluid simulations as well as the Hamilton-Jacobi equation in control and verification. |

Anthony Peirce | Anthony’s principal areas of research expertise are in the application of asymptotic and numerical analysis to industrial problems. Research topics have included optimal control of molecular motion, stability of reactive fronts propagating in layered porous media, analysis of the regularisation effect of microstructure on localisation phenomena in elasto-plastic models, and development of multipole expansion techniques for boundary integral models of large-scale fracture interactions. His most recent research efforts are focussing on the analysis of hydraulic fracture propagation, which is of considerable importance in the oil, gas, and mining industries. Anthony was an interim UKAAM Director from 1999 to 2000. |

### Recommended Courses

Students interested in Optimisation and Control research in the UKAAM are advised to take the following preliminary, specific and optional courses:

**Preliminary and Foundational Courses**

CPSC 302: Numerical Computation for Algebraic Problems

CPSC 303: Numerical Approximation and Discretization

MATH 340: Introduction to Linear Programming

MATH 401: Green’s Functions and Variational Methods

MATH 402: Calculus of Variations

MATH 403: Optimal Stabilization and Control of Dynamical Systems

MATH 405: Numerical Methods for Differential Equations

MATH 441: Mathematical Modeling: Discrete Optimization Problems

MATH 442: Optimization in Graphs and Networks

**Specific Courses**

CPSC 406: Computational Optimization

CPSC 546: Numerical Optimization

MATH 547: Optimal Control Theory

**Further Options**

MATH 523: Combinatorial Optimization

EOSC 550: Linear Inverse Theory

EOSC 555: Nonlinear Inverse Theory