PRIMES is a free, year-long after-school research and enrichment program for high school students, based at the Massachusetts Institute of Technology. It includes three main sections: MIT PRIMES offers research projects in math and computer science to students from Greater Boston; PRIMES-USA is a national math research program for high school juniors; and PRIMES Circle is a math enrichment section for urban public high school students from the Boston area. In collaboration with MIT Admissions, PRIMES also runs MathROOTS, a free two-week math enrichment residential summer program for high-potential high school students from underrepresented backgrounds or underserved communities. PRIMES has developed an innovative approach, based on the combination of learning and research, which allows high school students to learn advanced areas of math and science and to participate in cutting-edge research within a year-long timeframe. Projects are formulated by university faculty and mentored by graduate students and postdoctoral scholars. Every year, more than 90 students participate in PRIMES. They present their projects at an annual conference at MIT, open to the public; they write research and expository papers, posted online for free access; and they submit original research for publication in academic journals. PRIMES gives talented high school students a unique opportunity to experience the joy and beauty of mathematical research, inspires them to pursue careers in the mathematical sciences, and helps diversify the mathematical community by providing additional opportunities for promising young women and underrepresented groups.
In this project, PRIMES students will work on research projects on a variety of pure and applied mathematical topics, which include Branching types of rational functions; Statistics and combinatorics of curves on surfaces; Jacobians of finite graphs; Quasiinvariants; Representations of rational Cherednik algebras in positive characteristic; Folding random walks; Multi-crossing number for knots; Traffic modeling, multi-phase flow, and autonomous cars; Superalgebra in characteristic 2; Sets of permutations invariant under valley-hopping; and Pattern replacement equivalences of permutations. Reading groups will study texts on abstract algebra, the probabilistic method, Abel's Theorem, representation theory, analytic number theory, and cryptography. Enrichment topics will include knot theory, probability, game theory, graph theory, and combinatorics.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.