Research Opportunities for Students and Postdocs

I am always interested in attracting new students and postdocs who have a strong mathematical and computational background and are enthusiastic about applying what they know to solve real problems with a physical, biological or industrial application. My research broadly centers on mathematical modelling, where I take knowledge and techniques from applied mathematics and scientific computing such as . . .

Navier-Stokes equations (and more generally, nonlinear parabolic advection-diffusion-reaction equations), hyperbolic conservation laws,
asymptotic analysis, multiscale analysis and periodic homogenization,
linear stability analysis, approximation theory,
finite volume methods, semi-implicit time-stepping schemes, parallel algorithms

. . . and apply them to studying real applications in fluid dynamics, including . . .

Fluid-structure interaction: collective swimming dynamics, active suspensions,
Porous media flows: groundwater transport, concrete degradation,
Tree sap hydraulics: freeze/thaw-induced sap exudation, starch hydrolysis, plant-based bacterial infections.

• Do you have a degree in a discipline other than mathematics?
  I often take on MSc students who hold degrees from other disciplines, including computing science, physics, mechanical engineering and other closely-related fields. However, you must have taken at least some advanced (upper-division) courses in applied mathematics (e.g., PDE, real analysis, numerical analysis, etc.).

• Are you interested in doing a PhD under my supervision?
  Admission to SFU's PhD program in Applied and Computational Mathematics (APMA) has grad course prerequisites that are based on the APMA MSc, and so I usually prefer to take on doctoral students who have first gone through our APMA MSc program. If I do take on a student with a Master's from another university that is missing some equivalent coursework, then they are often admitted into the APMA MSc program for a "qualifying year" of sorts.

• What are your chances of being accepted in the MSc/PhD program under my supervision?
  I am unable to answer this question. These decisions are made by the Math Graduate Studies Committee and not by individual professors. Our admissions process is competitive, and so decisions depend on the quality of the applicant pool in any given year. Please review my department's information for graduate applicants and note that the deadline is January 15.

• What funding would you receive as a graduate student?
  Every student accepted into the MSc/PhD program receives a funding offer that is at least at the minimum levels outlined in my department's Graduate Student Funding Policy. Each year, this corresponds to two terms of work as a Teaching Assistant, plus one term paid from a Research Assistantship.

• Are you looking for a postdoctoral fellowship?
  I don't always have sufficient funds to fully support a postdoc, but I still encourage you to inquire with me. The PIMS Postdoctoral Fellowship (deadline on December 1) is one excellent opportunity for both domestic and international PDFs. If you are also a Canadian permanent resident, then I encourage you to apply for the NSERC Postdoctoral Fellowship (deadline in mid-October). Warning: both fellowships are extremely competitive and you must contact me well in advance of the deadlines.

• Is your primary interest in computational fluid dynamics (CFD)?
  Please understand that my approach to CFD is intrinsically mathematical and very different from engineering CFD. I do not use commercial CFD codes because they are largely unsuited for solving the complex, nonlinear, nonstandard problems in which I am interested. Instead, my students develop their own codes that implement custom algorithms specially-tailored to solve the problem at hand.

• Are you an undergrad looking for a summer research position or internship?
  I occasionally take on a summer research assistant, but you must see me in person to discuss any open opportunities. Undergraduate research projects in the Mathematics Department are announced usually in late November, and so the time to meet with me is early in the fall semester and well in advance of the January application deadline.