### Contact details:
My new name is apparently nna29.

If you found me by typing sfu.ca/~nna29, please tell my folks I'm OK.

**Email:** nigam at math dot sfu dot ca

** Office: **SC K10535

Dept. of Mathematics

Simon Fraser University

8888 University Drive,
Burnaby,
BC, V5A 1S6

Canada

**Phone:** 778-782-4258

**Fax:** 778-782-4947

### Research:

My main interests are in the areas of PDE and numerical analysis, with applications in computational electromagnetics, mathematical physiology and mechanics. Specifically, I
work on the development and analysis of numerical methods for scattering and spectral problems, including FEM and integral equation methods. Apart from this, I
enjoy using mathematics to solve real-world problems wherever they arise.

I currently serve on the editorial boards of the SIAM Journal on Scientific Computing, Mathematics-in-Industry Case Studies, Computers and Mathematics with Applications, SIAM News and Advances in Continuous and Discrete Models. I serve on the series editorial boards of the CMS/CAIMS Book Series in Mathematics, and the SIAM Book Series on Mathematics and Computation. I'm also a category co-moderator for the arXiV.
### Summer research opportunities

This summer, I'm welcoming students who are interested in undergraduate research to work with me on a couple of projects. You're encouraged to apply to the SFU Department of Mathematics USRA competition. I'm also happy to hear from interested+qualified students directly.
#### Muscles: from MRI data to biomechanics

Co-Supervisor: Professor James Wakeling, BPK
Muscles - in concert with tendons and other connective tissues - are critical to locomotion, and exhibit fascinating mechanical properties. There's great interest in the fields of muscle physiology as well as neuromuscular science around how the structure and composition of actual muscle tissue impacts muscle function. Mathematical models can provide a great deal of insight, and that's where our work lies. Medical imaging data (especially MRI data) of muscle-tendon units need to be translated into hexahedral meshes which are used as part of a discretization strategy for the equations governing the dynamics of muscle. Several questions arise: what are the mathematical conditions on allowable meshes? How do we ensure the meshes are topologically consistent? How does one robustly identify the directions of muscle fibres from MRI data? How does one (if at all) find thin sheets of connective tissue from the data?
You'll learn about both the physiological/medical questions which are driving these investigations, and the state-of-the-art discretization strategies we're using. Your work will be at the interface of mathematics, computer graphics and biomechanics, and you'll be part long-term collaboration with the Neuromuscular Lab in BPK. You'll be given access to code libraries to start building your ideas on.
Requirements (i.e. courses, skills, or qualities possessed by the ideal candidate): Prior experience in computing is required (Matlab OK, C++/Python preferred). Candidates should be very comfortable with the contents of strong undergraduate course in numerical analysis (316 minimally, 416 ideally) and ideally have some background in basic mechanics (either a physics, engineering or BPK course); a PDE course would be an asset. Since this is a highly interdisciplinary project, it's pretty unlikely anyone will have _all_ the necessary background; learning it is part of the project outcome. The ideal candidates will be curiosity-driven, motivated, and willing to read/learn independently.
#### Spectral geometry for the Steklov-Maxwell system

If you've taken a first PDE course, you've likely encountered the so-called Dirichlet eigenvalue problem for the Laplacian (the eigenfunctions are used in the the technique of separation-of-variables). In these, the eigenvalues depend quite strongly on the spatial domain. In Steklov eigenvalue problems, we seek eigenmodes of a given PDE operator (could be the Laplacian!) in which the eigenvalue relates the Dirichlet and Neumann data. In this project we'll first look at a mathematical statement of the Steklov eigenvalue problem for Maxwell's equations. Next, we'll frame and answer questions about how the geometric properties of the domain influence the spectrum.
Requirements (i.e. courses, skills, or qualities possessed by the ideal candidate): A strong background in vector calculus, analysis and PDE (Math 320 minimum, Math 314 minimum, Math 418 an asset). The ideal candidate will have had some exposure to electromagnetics, though this is not a requirement; a willingness to learn and read independently is a must.