Vertical Integration of Research and Education in the Mathematical Sciences - VIGRE: Research Focus Groups in Mathematics

DMS-0135345PI: Bruno L. Nachtergaele，加州大学戴维斯分校标题：数学研究焦点小组摘要加州大学戴维斯分校VIGRE项目提供一系列活动，旨在将研究数学的兴奋融入其本科，研究生和博士后项目的各个方面。为了实现这一目标，研究者和他们的同事正在组织多达四个研究焦点小组，以协调四个研究领域的活动。每个研究焦点小组包括常规教员、博士后、研究生和本科生。小组的研究领域每年都有所不同，这取决于教师和研究生的兴趣和专业知识。初步建议包括：1)几何和拓扑，包括计算方面；2)经典和量子多体系统动力学；3)数学生物学，包括蛋白质结构与功能、生物流体力学、生态空间模型等；4)离散数学，包括代数和几何组合学以及随机离散优化。研究焦点小组活动包括研究研讨会、阅读研讨会、研究项目和外展计划。作为该项目的一部分，还设立了一个实习计划。研究焦点小组的目标之一是向本科生介绍数学研究，为研究生在其研究生生涯早期与教师和博士后密切互动提供机制，并为博士后提供学习成功数学事业所需的领导技能的机会。研究焦点小组让参与者直接参与当前非常感兴趣的活跃研究领域。这可以让初学的学生在早期就专注于有前途的数学职业道路，并创造一个环境，让他们可以更有效地为这样的职业做好准备。VIGRE项目和研究焦点小组也是毕业生招聘新举措的重点。来自研究焦点小组和实习参与者的反馈用于修改加州大学戴维斯分校的数学本科和研究生课程。

DMS-0135345PI: Bruno L. Nachtergaele, UC DavisTitle: Research Focus Groups in MathematicsAbstractThe UCDavis VIGRE project offers a range of activities designed to integrate the excitement of research mathematics into every facet of its undergraduate, graduate and postdoctoral programs. To accomplish this, the investigators and their colleagues are running up to four Research Focus Groups as a means to coordinate the activities in four research areas. Each Research Focus Group includes regular faculty members, postdoctoral fellows, graduate students, and undergraduates. The areas of research of the Groups vary from year to year, depending on the interests and expertise of the faculty and graduate students. Initial proposals include: 1) Geometry and Topology, including Computational Aspects; 2) Dynamics of Classical and Quantum Many-Body Systems; 3) Mathematical Biology, including Protein Structure and Function, Biofluid Mechanics, and Spatial Models in Ecology; 4) Discrete Mathematics, including Algebraic and Geometric Combinatorics and Stochastic Discrete Optimization. The Research Focus Group activities include a research seminar, a reading seminar, research projects, and outreach programs. An internship program has also been set up as part of the project.Among the goals of the Research Focus Groups are to introduce undergraduates to mathematical research, to provide a mechanism for graduate students to interact closely with faculty and postdoctoral fellows early in their graduate careers, and to give postdoctoral fellows an opportunity to learn leadership skills necessary to a successful mathematical career. The Research Focus Groups offer participants direct involvement in active areas of research of great current interest. This allows beginning students to focus on a promising career path in mathematics early on, and creates an environment where they can be more effectively prepared for such careers. The VIGRE project and the ResearchFocus Groups also serve as a focus of new initiatives in graduate recruitment. Feedback from Research Focus Groups and internship participants is used to revise the mathematics undergraduate and graduate programs at UC Davis.