Photo of Kelly McQuighan
Instructor and Post Doctoral Visiting Assistant Professor
Department of Mathematics and Statistics
Boston University

111 Cummington Mall
Room: 234
Email: kmcquigh AT bu DOT edu

Office Hours: Tuesday/Thursday 10:45-12:15

I am one of the co-organizers for the joint Brown/BU PDE seminar.

Programming languages and packages: C/C++, Python, Matlab, Java, MPI, ScaLAPACK

Areas of Expertise

In my research I study the existence and stability of solutions to differential equations. I am particularly interested in studying how techniques from dynamical systems (such as ideas from invariant manifold theory) can be applied to partial differential equations (PDEs). I am particularly motivated by problems which arise in models of the physical world. For example, in my thesis work I provided an explaination for the formation of oscillons; recently I have been motivated by problems in fluid dynamics.

In the study of differential equations, it is not always clear what will be the fruitful mathematical questions. The first thing I often do in a new research project, therefore, is to simulate solutions to the PDE and look for interesting behavior. In an ongoing project with C. Eugene Wayne at Boston University we are attempting to find a good mathematical framework for explaining the metastable behavior exhibited by solutions to the periodic 2D Navier-Stokes equation, as shown in these simulations created by myself using Python. The result of this simulation was first reported on in Alternative statistical-mechanical descriptions of decaying two-dimensional turblence in terms of "patches" and "points" by Z. Yin, D. Montgomery, and H. Clercx, although when I re-created their simulations I observed a new direction for study.

I also have a background in High Performance Computing, including graduate level coursework at Brown University and a summer internship at Hypercomp. Additionally, I served as an Instructor and Group Mentor for the Kobe-Brown Simulation Summer School in August 2013. In preparation for the summer school I translated the DOE ACTS Fortran BLACS and ScaLAPACK examples into C for students to use as examples. You can download my C code here.

You can find examples of how I've used programming as an educational tool in the "About Me" section of my teaching page (in particular: the sections on "Providing students with tools" and "Projects").

Education

Work History

Summer Internships

Awards and Honors