# MIT PRIMES: Areas of Research

2020 Research Areas

In 2020 MIT PRIMES runs research projects in mathematics, computer science, bioinformatics, and computational biology.

**Mathematics**

The local section has 22 students working on 3 research projects (1 individual and 2 joint projects for 3 students) and studying in 5 reading groups (3 students each) The national PRIMES-USA Math section has 40 students working on 24 research projects (19 individual and 5 joint projects for 3 students) and studying in 2 reading groups (3 students each). Mathematics research projects for PRIMES were suggested by faculty and researchers from MIT, Brandeis University, CUNY – City College, Iowa State, New York University, University of Cambridge (UK), University of Illinois at Chicago, University of Michigan, UMass Amherst, and MathWorks. They include projects in combinatorics, algebraic combinatorics, algebra, computer algebra, graph theory, voting theory, and number theory.

For more detail, see

Pavel Etingof, Slava Gerovitch, and Tanya Khovanova, Mathematical Research in High School: The PRIMES Experience, *Notices of the AMS*, 62 (2015)

**Computer Science**

This section has 20 students working on 18 research projects (16 individual and 2 joint projects for 2 students). Computer science research projects for PRIMES were suggested by faculty from MIT Computer Science and Artifical Intelligence Laboratory, UMass Lowell, and Tufts University. They include projects in data protection, network security, operating systems, natural language processing, machine learning and deep learning, and robotics.

**Bioinformatics and Computational Biology**

This section has 11 students working on 9 research projects (6 individual projects and 3 joint projects). Bioinformatics and computational biology research projects for PRIMES were suggested by researchers from the Mirny Lab at MIT, Biomedical Cybernetics Laboratory and the Kwon Lab at Harvard Medical School, and the Broad Institute of MIT and Harvard.

On the work of the Mirny Lab, see news articles:

*DNA's secret weapon against knots and tangles* (2017)

*Study: Molecular motors shape chromosome structure* (2016)

*Some cancer mutations slow tumor growth* (2013)

* Seeing cancer in three dimensions* (2011)

2019 Research Areas

In 2019 MIT PRIMES offered research projects in mathematics, computer science, bioinformatics, and computational biology.

**Mathematics**

The local section had 26 students working on 11 research projects (10 individual projects and 1 joint project for 2 students) and studying in 6 reading groups. The national PRIMES-USA Math section had 16 students working on individual research projects. Mathematics research projects for PRIMES were suggested by faculty and researchers from MIT, Brandeis University, CUNY – City College, Harvard, Iowa State, University of Cambridge (UK), University of Illinois at Chicago, University of Minnesota in Minneapolis, and MathWorks. They included projects in combinatorics, algebraic combinatorics, algebra, computer algebra, graph theory, voting theory, and number theory.

**Computer Science**

This section had 20 students working on individual research projects. Computer science research projects for PRIMES were suggested by faculty from MIT Computer Science and Artifical Intelligence Laboratory and Cloud Computing Initiative at Boston University. They included projects in data protection, network security, operating systems, machine learning and deep learning, and robotics.

**Bioinformatics and Computational Biology**

This section had 15 students working on 11 research projects (8 individual projects and 3 joint projects for 2-3 students). Bioinformatics and computational biology research projects for PRIMES were suggested by researchers from the Mirny Lab at MIT, Biomedical Cybernetics Laboratory at Harvard Medical School, and the Broad Institute of MIT and Harvard.

2018 Research Areas

In 2018 MIT PRIMES offered research projects in mathematics, computer science, and computational biology.

**Mathematics**

The local section had 28 students working on 11 research projects (8 individual projects and 3 joint projects for 2-3 students) and studying in 6 reading groups. The national PRIMES-USA Math section had 21 students working on 18 research projects (16 individual projects and 2 joint projects for 2-3 students). Mathematics research projects for PRIMES were suggested by faculty and researchers from MIT, CUNY – City College, Penn State, University of Illinois at Chicago, UMass Amherst, and MathWorks. They included projects in combinatorics, algebraic combinatorics, algebra, computer algebra, graph theory, voting theory, and number theory.

**Computer Science and Computational Biology**

This section had 27 students working on 21 research projects (15 individual projects and 6 joint projects for 2 students). Computer science and computational biology research projects for PRIMES were suggested by faculty from MIT Electrical Engineering and Computer Science Department, Biomedical Cybernetics Laboratory at Harvard Medical School, Cloud Computing Initiative at Boston University, and the Broad Institute of MIT and Harvard. They included projects in data protection, network security, operating systems, computational biology, and biomedical informatics.

2017 Research Areas

In 2017 MIT PRIMES offered research projects in mathematics, computer science, and computational neuroscience and biology.

**Mathematics**

The local section had 25 students working on 10 research projects (6 individual projects and 4 joint projects for 2 students) and studying in 5 reading groups. The national PRIMES-USA Math section had 19 students working on individual research projects. Mathematics research projects for PRIMES were suggested by faculty from MIT, Cornell University, Boise State University, Brandeis University, CUNY – City College, SUNY at Stony Brook, University of Illinois at Chicago, University of Michigan, University of Washington, and MathWorks. They included projects in combinatorics, algebraic combinatorics, algebra, computer algebra, graph theory, and number theory.

**Computer Science and Computational Neuroscience and Biology**

This section had 29 students working on 20 research projects (13 individual projects and 7 joint projects for 2-3 students). Computer science research projects for PRIMES were suggested by faculty from MIT Electrical Engineering and Computer Science Department, Biomedical Cybernetics Laboratory at Harvard Medical School, Synthetic Neurobiology Group at MIT Media Lab, Cloud Computing Initiative at Boston University, the Broad Institute of MIT and Harvard, and IPG Photonics Corporation. They included projects in data protection, network security, operating systems, robotics, computational neuroscience, computational biology, and biomedical informatics.

2016 Research Areas

In 2016 MIT PRIMES offered research projects in mathematics, computer science, and computational and physical biology.

**Mathematics**

The local section had 19 students working on 6 research projects (5 individual projects and 1 joint project for 2 students) and studying in 6 reading groups. The national PRIMES-USA Math section had 17 students working on individual research projects. Mathematics research projects for PRIMES were suggested by faculty from MIT, Stanford University, the University of Michigan, the University of Illinois at Chicago, SUNY at Stony Brook, CUNY – City College, and MathWorks. They included projects in combinatorics, algebraic combinatorics, algebra, computer algebra, graph theory, and number theory.

**Computer Science**

This section had 21 students working on 13 research projects (8 individual projects and 5 joint projects for 2-3 students). Computer science research projects for PRIMES were suggested by faculty from MIT Electrical Engineering and Computer Science Department, Biomedical Cybernetics Laboratory at Harvard Medical School, Synthetic Neurobiology Group at MIT Media Lab, and Cloud Computing Initiative at Boston University. They included projects in data protection, network security, operating systems, and biomedical informatics.

**Computational and Physical Biology**

This section had 4 students working on individual projects on genomic and epigenomic signatures of chromosomal domains and on the integrative analysis of genomic and functional data for cancer cell lines. Computational and physical biology projects for PRIMES were run by the Mirny Lab and by the Broad Institute of MIT and Harvard.

2015 Research Areas

In 2015 MIT PRIMES offered research projects in mathematics, computer science, and computational and physical biology.

**Mathematics**

The local section had 20 students working on 10 research projects (9 individual projects and 1 joint projects for 3 students) and studying in 4 reading groups. The national PRIMES-USA Math section had 16 students working on 14 research projects (13 individual projects and 1 joint project for 3 students). Mathematics research projects for PRIMES were suggested by faculty from MIT, the University of Michigan, the University of Illinois at Urbana-Champaign, SUNY at Stony Brook, CUNY – City College, and MathWorks. They included projects in combinatorics, algebraic combinatorics, algebra, computer algebra, graph theory, and number theory. For details, see project presentations at the 2015 PRIMES Conference.

**Computer Science**

This section had 21 students working on 14 projects (8 individual projects and 6 joint projects for 2-3 students). Computer science research projects for PRIMES were suggested by faculty from MIT Electrical Engineering and Computer Science Department, the Harvard-MIT Health Sciences and Technology Division, and the Draper Lab. They included projects in data protection, computational biology, genomics interface design, and medical informatics. For details, see project presentations at the 2015 PRIMES Conference.

**Computational and Physical Biology**

This section had 2 students working on a joint project on genomic and epigenomic signatures of chromosomal domains. Computational and physical biology projects for PRIMES are run by the Mirny Lab and funded by the MIT Physical Sciences-Oncology Center: Single-Cell Dynamics in Cancer. For details, see the project presentation at the 2015 PRIMES Conference.

2014 Research Areas

In 2014 MIT PRIMES offered research projects in mathematics, computer science, and computational and physical biology.

**Mathematics**

The local section included 19 students working on 9 research projects (7 individual projects and 2 joint projects for 2 students) and studying in 4 reading groups. The national PRIMES-USA Math section had 13 students working on 11 research projects (10 individual projects and 1 joint project for 3 students). Mathematics research projects for PRIMES were suggested by faculty from MIT, Harvard University, Brandeis University, the University of Massachusetts (Lowell), and MathWorks. They included projects in combinatorics, algebraic combinatorics, algebra, computer algebra, graph theory, and number theory. For details, see project presentations at the 2014 PRIMES Conference.

**Computer Science**

This section included 15 students working on 10 projects (5 individual projects and 5 joint projects for 2 students). Computer science research projects for PRIMES were suggested by faculty from MIT Electrical Engineering and Computer Science Department and the Harvard-MIT Health Sciences and Technology Division. They included projects in data protection, functional programming for web apps, natural language processing, computational biology, genomics interface design, and medical informatics. For details, see project presentations at the 2014 PRIMES Conference.

**Computational and Physical Biology**

This section included 2 students working on individual projects. Computational and physical 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 the impact of bound protein on the sub-diffusion of a DNA locus and dynamic folding of chromatin domains. For details, see project presentations at the 2014 PRIMES Conference.

2013 Research Areas

In 2013 MIT PRIMES offered research projects in mathematics, computer science, and computational and physical biology.

**Mathematics**

The local section included 19 students working on 12 research projects (10 individual projects and 2 joint projects for 2 students) and studying in 3 reading groups (1-2 students in each). The national PRIMES-USA Math section had 5 students working on 5 individual research projects. Mathematics research projects for PRIMES were suggested by faculty from MIT, Harvard University, Brandeis University, the University of Massachusetts (Lowell), and MathWorks. They included projects in combinatorics, algebraic combinatorics, algebra, computer algebra, graph theory, and number theory. For details, see project presentations at the 2013 PRIMES Conference.

**Computer Science**

This section included 16 students working on 12 projects (8 individual projects and 4 joint projects for 2 students). Computer science research projects for PRIMES were suggested by faculty from MIT Electrical Engineering and Computer Science Department, the Harvard-MIT Health Sciences and Technology Division, and Draper Laboratories. They included projects in concurrent data structures, algorithmic game theory, machine-checked mathematical theorem-proving, functional programming for web apps, computational biology, and medical informatics. For details, see project presentations at the 2013 PRIMES Conference.

**Computational and Physical Biology**

This section included 4 students working on individual projects. Computational and physical 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 2013 PRIMES Conference.

2012 Research Areas

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

**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, Brandeis University, 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

In 2011 MIT PRIMES offered research projects in mathematics and computational and physical biology

**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.

**Contact**

**With questions, contact PRIMES Program Director
Dr. Slava Gerovitch at**** primes@math.mit.edu **