MIT PRIMES is a free, year-long research program for high school students. This proposal requests funding for research projects on representations of symplectic reflection algebras in positive characteristic, representations of continuous Hecke algebras in positive characteristic, the structure of lower central series of associative algebras defined by generators and relations, the structure of ideals generated by terms of the lower central series defined by generators and relations, thracklability of graphs, decay of crossing numbers, Ramsey multiplicity, the visibility conjecture, the Richter-Thomassen conjecture, and coinvariants of incompressible vector fields.
PRIMES students will work on their projects during the academic year, aided by weekly meetings with their mentors (MIT Mathematics Department graduate students) on the MIT campus. The projects will be presented at annual PRIMES conferences, and final papers will be posted on the Program website and disseminated through arXiv.org and academic journals. Participation in PRIMES would help talented high school students discover the beauty of mathematical research and would inspire them to choose careers in the mathematical sciences. A special section of PRIMES, called PRIMES Circle, will be dedicated to serving students from urban high schools. PRIMES Circle students would learn an advanced mathematical topic in a challenging academic environment through directed reading and problem-solving. This would serve as preparation for further research and encouragement for pursuing degrees in the mathematical sciences.
