Center for Mathematics at Notre Dame

2018年圣母大学数学中心项目将由三个项目组成，于2018年6月11日至29日在圣母大学举行。这三个项目包括6月11日至15日的本科生暑期班，6月18日至22日的研究生暑期班，以及6月25日至29日的几何表示理论和辛型变化会议。该课程的目的是向不同层次的学生介绍几何表示理论中的重要思想，几何表示理论是数学中一个活跃而重要的领域。第一周的目标是让本科生接触到他们通常在研究生之前看不到的基本思想。我们将通过讲座和积极学习相结合的方式介绍材料，目的是激励学生在未来的学习中参加高级课程或阅读课程。第二周和第三周将包括面向该领域研究生的暑期学校，随后将举行一次会议，介绍在第二周开发的主题的当前研究。第二周的目标是鼓励研究生探索不同数学领域之间的联系，超越他们在自己的研究生课程中看到的水平。我们还希望将来自不同机构的研究生和博士后聚集在一起，这样他们就可以发展富有成效的职业关系。我们注意到，圣母大学以前的数学中心项目的许多学生都获得了数学博士学位，2018年会议上的一名特邀演讲者作为研究生参加了我们2011年的项目。几何表示理论和辛变体项目的目标是将在这些领域工作的研究人员聚集在一起，使这些技术能够为广大观众所接受。第一周将讨论广义旗簇及其几何，以及sl(2)的Beilinson-Bernstein对应。第二周将介绍辛分解几何表示理论的基本思想，并包括该领域公认专家的系列讲座。第三周将包括一场关于该项目主题的国际会议，并将介绍对研究生暑期学校的许多想法的最新研究。该计划的网站为www.w3.nd.edu/~cmnd/Programs/cmnd2018/。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The 2018 Center for Mathematics at Notre Dame program will consist of a series of three programs, held from June 11 to 29 of 2018 at the University of Notre Dame. The three programs include an undergraduate summer school June 11-15, a graduate summer school June 18-22, and a conference on Geometric Representation Theory and Symplectic Varieties June 25-29. The purpose of the program is to introduce students at various levels to important ideas in geometric representation theory, which is an active and important area of mathematics. The goal of the first week is to expose undergraduates to fundamental ideas they would not normally see until graduate school. We will introduce material through a combination of lectures and active learning sessions, with the aim of inspiring students to take advanced courses or reading courses in their future studies. The second and third weeks will consist of a summer school geared towards graduate students in the field, followed by a conference that will present current research on topics developed in the second week. The goal of the second week is to inspire graduate students to explore connections between different areas of mathematics, beyond the level they may see in their own graduate program. We also hope to bring together graduate students and postdocs from different institutions so they can develop productive professional relationships. We note that many students from previous Center for Mathematics at Notre Dame programs have gone on to get a Ph.D. in mathematics, and one invited speaker at our 2018 conference attended our 2011 program as a graduate student.The goal of the program Geometric Representation Theory and Symplectic Varieties is to bring together researchers working in these areas and make these techniques accessible to a broad audience. The first week will discuss generalized flag varieties and their geometry, as well as the Beilinson-Bernstein correspondence for sl(2). The second week will expose basic ideas from geometric representation theory of symplectic resolutions, and includes lecture series by recognized experts in the field. The third week will consist of an international conference on the program topic, and will present current research on many of the ideas from the graduate summer school. The program website is available at www3.nd.edu/~cmnd/programs/cmnd2018/.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.