REU Site: Research in Geometry, Algebra, and Analysis

一个积极的和多样化的本科生群体将被招募工作的研究问题，在各种数学主题，包括几何和分析。该计划的目的是为有才华和有动力的本科生提供数学研究经验。学生将从事数学系教师研究中自然产生的项目。学生参与者将学习如何讨论和提出数学思想，撰写项目报告，探索数学软件，并从事数学研究。该计划的重点是在项目顾问的密切监督下独立工作。该计划将提供一个激烈的研究生院般的经验，并引导学生认识和欣赏数学的不同领域之间的潜在联系。该方案将在全国范围内进行宣传，特别努力接触代表性不足的群体。我们期望许多REU学生将决定攻读数学或相关领域的研究生课程。大多数项目只需要有限的背景，允许参与者在研究问题的同时扩展他们对该学科的知识。这也将有助于在学习的早期阶段招收准备充分的学生，包括大一和二年级学生。项目的动机将来自各个领域，包括代数几何，编码理论，凸几何，群论，调和分析，格点几何，李代数，线性代数，数论，算子理论和环理论。所有的项目都将处理未解决的研究问题。根据以往的经验，预计许多项目将导致在参考期刊上发表文章。

A motivated and diverse group of undergraduates will be recruited to work on research problems in a variety of topics in mathematics including geometry and analysis. The purpose of the program is to provide mathematics research experiences in a nurturing atmosphere for talented and motivated undergraduates. Students will work on projects arising naturally in the research of the Mathematics Department faculty. The student participants will learn how to discuss and present mathematical ideas, write project reports, explore with mathematical software, and engage in mathematical research. The emphasis of the program is on independent work under close supervision of a project advisor. The program will provide an intense research graduate school-like experience and lead students to awareness and appreciation for potential connections between different fields of mathematics. The program will be advertised nationally with a particular effort to reach underrepresented groups. The expectation is that many of the REU students will decide to pursue graduate studies in mathematics or related fields.Most of the projects will require only a limited background, allowing the participants to get right to work extending their knowledge of the subject while working on research questions. This will also allow for the recruitment of well-prepared students at earlier stages of their studies, including freshmen and sophomores. Motivations for the projects will come from a variety of fields, including algebraic geometry, coding theory, convex geometry, group theory, harmonic analysis, lattice point geometry, Lie algebras, linear algebra, number theory, operator theory, and ring theory. All the projects will deal with unsolved research problems. Based on previous experience, the expectation is that many of the projects will lead to publications in refereed journals.