PRIMES: Areas of Research

2013 Research Areas

Research Fields in Mathematics

For more detail, see

World-class research … in the 10th grade (MIT News article)

Research Fields in Computer Science

• concurrent data structures
• algorithmic game theory
• machine-checked mathematical theorem proving
• functional programming for web apps
• computational biology
• medical informatics

Computational and Physical Biology

Computational biology projects for PRIMES were run by the Mirny Lab and funded by the MIT Physical Sciences-Oncology Center: Single-Cell Dynamics in Cancer. Research on this track involved large-scale computer simulations and required spending substantial time at a computer lab on the MIT campus. Research topics included studying mutations that cause cancer, studying the evolutionary origins of genes that cause cancer, and studying how a long DNA or RNA molecule is packed inside a tiny virus particle. For details, see project presentations at the 2012 PRIMES Conference.

On the work of the Mirny Lab, see MIT News articles:

Some cancer mutations slow tumor growth (2013)

Seeing cancer in three dimensions (2011)

 

The choice of research topics will depend on the background and preferences of PRIMES participants.

2012 Research Areas

In 2012 PRIMES offered research projects in mathematics, computational and physical biology, and computer science.

Projects in Mathematics

This section included 16 students working on 12 projects (8 individual projects and 4 joint projects for 2 students). Mathematics research projects for PRIMES were suggested by faculty from MIT, the University of Massachusetts (Lowell), and MathWorks. They included projects in combinatorics, graph theory, analysis, dynamical systems, number theory, group theory and representation theory. For details, see project presentations at the 2012 PRIMES Conference.

Computer Science

This section included 10 students working on 8 projects (6 individual projects and 2 joint projects for 2 students). Computer science research projects for PRIMES were suggested by faculty from MIT Electrical Engineering and Computer Science Department and from the Harvard-MIT Health Sciences and Technology Division. They included projects in distributed algorithms, computational complexity, programming languages, robotics, and medical informatics. For details, see project presentations at the 2012 PRIMES Conference.

Computational and Physical Biology

This section included 4 students. Computational biology projects for PRIMES were run by the Mirny Lab and funded by the MIT Physical Sciences-Oncology Center: Single-Cell Dynamics in Cancer. Research topics included studying mutations that cause cancer, studying the evolutionary origins of genes that cause cancer, and studying how a long DNA or RNA molecule is packed inside a tiny virus particle. For details, see project presentations at the 2012 PRIMES Conference.

2011 Research Areas

Projects in Mathematics

This section included 9 students working on 8 projects (7 individual projects and 1 joint project for 2 students). Mathematics research projects for PRIMES were suggested by faculty from MIT, the University of Massachusetts (Lowell), and Microsoft Research New England. They included projects in combinatorics, graph theory/dynamical systems, arithmetic of finite fields, commutative algebra and algebraic geometry over finite fields, number theory, convex geometry, and representation theory. For details, see project presentations at the 2011 PRIMES Conference and the 2011 research papers.

Computer Algebra Lab

This was a workshop for 6 students. The goal of the Lab was to teach the students the basics of abstract algebra in a hands-on way through the use of the advanced computer algebra system SAGE. At the same time, the students learned how to use SAGE to obtain experimental data in algebra problems. The Lab students were working on 3 research projects (1 individual and 2 group projects) on representation theory. For details, see project presentations at the 2011 PRIMES Conference and the 2011 research papers.

Computational and Physical Biology

This section included 6 students. Computational biology projects for PRIMES were run by the Mirny Lab and funded by the MIT Physical Sciences-Oncology Center: Single-Cell Dynamics in Cancer. The projects included a study of the role of cell function in cancer progression by computer simulations and the use of molecular dynamics simulations for 3-D DNA data analysis. For details, see project presentations at the 2011 PRIMES Conference.

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