Dear prospective student:

I have supervised more than 35 PhD students so far, and I know that the decision to attend graduate school is a tough one, but so is the decision in selecting a PhD topic- this will define the rest of your life! In the CRUNCH group we are combining applied mathematics and powerful supercomputers to tackle some of the most difficult open problems in physical and life sciences that involve differential equations in time, space or random dimensions. We focus on stochastic multiscale modeling and we pay attention to both the algorithms as well as the applications. We are branching out to new unexplored areas of computational science and engineering, developing new mathematical formulations (i.e., new differential equations) for the first time, e.g. in the new area of neurovascular coupling in the brain. Our group is perhaps one of the most diverse and interdisciplinary scientific computing groups in the world in that respect, developing state-of-the-art numerical methods for new problems but also studying in depth interesting applications in biophysics and engineering. Our curent interest is on stochastic PDES and also on multiscale modeling for biomedical problems, involving multiple spatial and temporal scales, thus requiring the coupling of heterogeneous descriptions and corresponding numerical methods (e.g. PDEs and molecular dynamics). I invite you to read more details about some of our current projects on the crunch website. You can also check the quality of our publications on three different projects: Stochastic PDEs, Multi-Scale Modeling, Biophysics, Turbulence, and Shock Dynamics. Click here to read a review article on Stochastic CFD.

We are a relatively big group - more than 10 PhD students, a few postdocs and visitors in steady state - but we always have openings for new (and good) PhD students. We do not admit Masters' students but we like to include undergraduates in some of our projects. We have formed a multidisciplinary group by working closely with other Brown faculty across different fields including the Medical School . In fact, many of the PhD students usually have more than one advisor. Some of the students pursue dual degrees, e.g. PhD in Applied Mathematics with Masters in Computer Science. We also share postdocs with MIT and Harvard Medical School and we have close collaborations and joint projects with research groups both at MIT and Harvard. There are many international visitors in the group who interact closely with the PhD students. I like to work with PhD students from different backgrounds, i.e., mathematics, computer science, physics, engineering, biology or chemistry and some of my current PhD students have such diverse backgrounds. In the CRUNCH group we make the PhD student the leader of a particular project so we rely on self-motivating and hard-working dedicated individuals. This is the most important criterion for joining the crunch group: self-motivation and love for computational mathematics!

Before you choose an advisor, check what happened to PhD students graduated from that group - where are they now?....The students who have graduated from CRUNCH are now leaders in academia (Purdue University, Imperial College, Paris VI, U Minnesota, etc...) and industry. For example, Cait Crawford currently at IBM was named in the top ten list of women in high tech to watch for designing the first petaflop computer. Also, Dmitry Fedosov received the Nicholas Metropolis award in 2011 for the best doctoral thesis work in computational physics. My first PhD student, Ron Henderson is the director of computer graphics at Dreamworks, making movies like Kung Fu Panda, using multiscale simulations...Now that's a lot of fun!

If you believe that you are such an individual and you want to join CRUNCH please contact me directly ( or contact Ms. Jean Radican ( for more details regarding the application procees to the Division of Applied Mathematics at Brown University.

Thanks (Xie-Xie) for visiting and good luck!

George Em Karniadakis