Students applying to the DOE CSGF Mathematics/Computer Science (Math/CS) Track must be pursuing a doctoral degree in applied mathematics, statistics, computer science, computer engineering or computational science — in one of these departments or their academic equivalent. A departmental exception is made for students whose research is focused on algorithms or software for quantum information systems (QIS*) and who are enrolled in a science or engineering field. In all cases, research must contribute to more effective use of emerging high-performance computer systems.

Whereas individuals interested in the fellowship's Science & Engineering Track must have a specific science or engineering application for their research, Math/CS Track candidates are expected to focus on fundamental research into enabling technologies that are broadly relevant to science and engineering applications of interest to the DOE.

Such areas include (but are not limited to):

Applied and Mathematics and Statistics

  • ODE, PDE, and integral discretization methods
  • Scalable linear and nonlinear solvers
  • Multiscale, multi-physics coupling methods
  • Algorithms for quantum systems
  • Verification, validation, and uncertainty quantification
  • Scalable mathematical optimization methods
  • Machine learning fundamentals

Data Science

  • In situ data analysis
  • High-dimensional data analysis
  • Large-scale data visualization
  • Scientific data management and engineering

Computer Science and Computer Engineering

  • High-performance compilers
  • Domain-specific languages
  • Dynamic runtime environments
  • Power management
  • Novel HPC hardware technology
  • Programming models and abstractions for heterogeneous computing
  • HPC development tools and debugging at an extreme scale
  • HPC performance analysis and tools
  • Scalable I/O
  • Machine learning

Note that the interdisciplinary program of study (POS) requirement for Math/CS Track fellows is the same as for the Science & Engineering track, and includes science and engineering course requirements. The intent of this requirement is to ensure that the fellow is exposed to the computational needs of science and engineering applications that will use these new broadly applicable methods and technologies. Thus, the science and engineering courses in the POS will normally come from courses in the physical and biological sciences, or engineering disciplines such as mechanical or chemical engineering. POS courses from computer science or computer engineering departments must be listed under Computer Science and Computer Engineering and cannot be listed as Science & Engineering Applications.

* Students in the emerging field of QIS, which includes quantum computing, should choose carefully between the Math/CS Track and the Science & Engineering Track. Presently, much QIS research involves technology design and development and is carried out in physics departments. Students pursuing this line of QIS research, which makes use of scientific computing for the design and/or control of quantum information systems, should apply to the Science & Engineering track. Students who wish to apply for the Math/CS Track must be pursuing research focused on algorithms or software for QIS. Additionally, the Math/CS Track is open to students pursuing research in algorithms or software for quantum systems in a physics department.

Please contact Krell Institute staff with related questions prior to submitting an application.