Opportunities

Overview

I am always looking for talented undergraduate, graduate and postdoctoral researchers to join my group.  If you are a prospective student or postdoc please take a look at my Research page to get an overview of the type of research my group does. You may also want to check out this recent interview with SFU Science. If this work interests you, then please send me an email.

Opportunities

Here is a list of opportunities broken down by category:

Postdocs

No specific position at the moment.  But interested potential postdocs are welcome to contact me.

Graduate Students

Prospective MSc and PhD students who wish to work in my group need to apply to the SFU Mathematics graduate program.  If you are considering applying please email me to discuss your application further.   You are encouraged to submit your application by January 15, 2018.

Undergraduate Students

MITACS Globalink: I have several projects in the 2018 MITACS Globalink Research Internship program.  This program offers funding for 12-week summer research projects for senior undergraduate students.  Please check out http://mitacs.ca/en/programs/globalink for details.

SFU USRA/VPR: I typically host several undergraduate projects as part of the USRA/VPR program (for students from both SFU and elsewhere).  These are normally advertised in December on the SFU Mathematics website.  Several example projects are listed below:

1. Fast simulation of anomalous diffusion processes

Supervisors: Ben Adcock & Simone Brugiapaglia

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The goal of this project is to implement a fast Matlab solver for integro-differential equations involving the Fractional Laplace operator. These equations are able to model anomalous diffusion processes and have been recently used in many applications such as material science, finance, bioengineering, continuum mechanics, graph theory, and machine learning.

In this case, classical numerical schemes such as the finite element method may be very inefficient. Indeed, they require the storage of large-sized densely populated matrices that waste memory and computational resources. In order to speed up the numerical computations, the idea is to employ some recent advanced techniques based on computational harmonic analysis and compressed sensing. These methods are able to exploit the sparsity of the solution with respect to a suitable set of basis functions and to compress the discretization using “short and fat” matrices, which are less demanding in terms of memory and more computationally tractable.

Proficiency with Matlab and familiarity with basic concepts of functional and numerical analysis are required. Previous knowledge of the finite element method is useful, but not mandatory.

 

2. Parameter estimation and uncertainty quantification via high-dimensional approximation in irregular domains

Supervisor: Ben Adcock

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Details to be added soon. 

 

3. Numerical methods for parameter assessment from time-dependent Magnetic Resonance signals

Supervisor: Ben Adcock

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Data from MRI scans is typically used to produce images that are interpreted for diagnosis.  However, there is substantial amounts of information in the data that is not extracted during the image formation process.  Discarded information such as temperature change, blood flow velocity, perfusion, diffusion, structure and physiology can provide practitioners with much broader clinical insight into the patient.

The purpose of this project is to develop numerical methods for extracting this information.  A major difficulty in extracting this information is that it requires the solution of a nonlinear and ill-posed inverse problem, which means that standard numerical methods typically produce poor reconstructions.  Nevertheless, progress has recently been made by exploiting the sparsity of the underlying quantities so as to regularize the underlying problems.  Aiming to enhance reconstruction fidelity, this project will explore the further development of these techniques.  Three particular areas of focus will be (i) the extension from single-coil to multiple-coil (i.e. parallel) MRI, (ii) the development of new gridding strategies for dealing with nonuniformly-acquired data, and (iii) the implementation of novel joint sparsity-promoting regularizers.

Linear algebra, numerical analysis and Matlab are essential.  Basic optimization and Fourier transforms are useful.