REU Site in Mathematics at Louisiana State University

路易斯安那州立大学的REU数学网站将邀请12名国家挑选的、高度积极的本科生围绕以下主题进行当前的数学研究：伽罗瓦理论、几何和纽带理论中的不变量。为此，我们将创造一个社会和科学活动的环境，培养智力创造力，鼓励相互支持，促进数学思想的讨论、交流和传播。学员被介绍到数论、代数几何和拓扑学领域的主流数学问题，这些领域得到了成熟的符号计算软件的支持。这提供了在理论知识进一步发展的同时提出重要问题和进行计算探索的早期能力。在辅导会议期间提供了额外的指导，允许每个参与者在第一周结束时选择自己的项目方向(在第一周介绍性陈述所展示的领域内)。REU的学生住在路易斯安那州立大学的校园里；计划开展更多的项目活动，以促进所有参与者的互动，并促进团队凝聚力。每个学生做几次毕业报告，并提交一份适合出版的书面论文。伽罗瓦理论、代数几何和纽结理论处于当前数学研究的许多线索的交汇点，连接着21世纪的几何问题。使用代数和计算工具来区分可能的几何结构。我们正在向新一代数学家介绍这种令人兴奋的想法组合，并为与会者提供适合在会议上发表演讲的沟通技能，以及关于申请研究生院和潜在职业机会的建议。通过扩大和加强受过数学培训的劳动力，REU将尽其所能缓解目前和预计的国家科技劳动力短缺问题。

The REU Site in Mathematics at the Louisiana State University will engage a group of twelve nationally selected, highly motivated undergraduates in current mathematical research around the theme: Invariants in Galois Theory, Geometry and Knot theory. To this end we will create an environment with social and scientific activities that nurtures intellectual creativity, encourages mutual support and promotes the discussion, communication and dissemination of mathematical ideas. Participants are introduced to mainstream math problems within the fields of number theory, algebraic geometry and topology which are supported by well-developed symbolical computation software. This provides an early capability to ask significant questions and make computational explorations while theoretical knowledge is being further developed. Additional guidance is provided during mentoring sessions to permit each participant to choose their own project direction at the end of the first week (within the arenas laid out by the introductory presentations during the first week). The REU students are housed on the LSU campus; additional program activities are planned that will foster the interaction of all participants and promote group cohesion. Each student gives several graduated presentations and submits a written paper in a form suitable for publication.Galois theory, algebraic geometry and knot theory lie at the intersection of many threads of current mathematical research connecting geometric problems of the twenty-first century. Algebraic and computation tools are employed to differentiate among the possible geometric structures. We are introducing a new generation of mathematicians to this exciting mix of ideas and providing participants with communication skills suitable to making presentations at conferences as well as advice on making applications to graduate school and on potential career opportunities. By broadening and strengthening the mathematically trained workforce, this REU will do its share to alleviate the current and projected national shortage within the scientific and technological workforce.