MIT PRIMES: Program for Research In Mathematics, Engineering, and Science for High School Students

MIT PRIMES是一个免费的，为期一年的高中生研究计划。该提案要求为以下研究项目提供资金：正特征辛反射代数的表示，正特征连续Hecke代数的表示，由生成元和关系定义的结合代数的下中心系列的结构，由生成元和关系定义的下中心系列项生成的理想的结构，图的thracklability，交叉数的衰减，Ramsey多重性，可见性猜想，Richter-Escherassen猜想和不可压缩向量场的coinvariants。PRIMES学生将在学年期间完成他们的项目，并在麻省理工学院校园与他们的导师（麻省理工学院数学系研究生）每周举行会议。这些项目将在年度PRIMES会议上提出，最后的论文将张贴在该方案的网站上，并通过arXiv.org和学术期刊传播。参加PRIMES将帮助有才华的高中生发现数学研究的美丽，并激励他们选择数学科学的职业。PRIMES的一个特殊部分，称为PRIMES圈，将致力于为城市高中的学生提供服务。PRIMES Circle的学生将通过指导性阅读和解决问题的方式，在充满挑战的学术环境中学习高级数学主题。这将作为进一步研究的准备，并鼓励攻读数学科学学位。

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.