Summer Programs on Commutative Algebra and Its Interactions with Algebraic Geometry and on p-adic L-functions and Eigenvarieties

圣母大学数学中心将在2019年开展一个关于交换代数及其与代数几何相互作用的项目，并在2020年开展一个关于p进l函数和特征变的项目。2019年，该项目将包括5月28日至6月1日的本科生暑期学校、6月3日至6月14日的研究生暑期学校、6月16日至6月21日的国际研究会议。2020年，该项目将包括为期一周的本科暑期学校、为期一周的研究生暑期学校和为期一周的会议。这些课程的目的是向不同层次的学生介绍交换代数和数论的重要思想，这些都是数学的活跃和核心领域，与其他数学和科学领域有许多联系。本科生周的目标是让本科生接触到他们在研究生院之前通常不会看到的基本思想。我们将通过讲座和主动学习课程相结合的方式来介绍材料，目的是激励学生在回到大学后参加高级课程或阅读课程。研究生暑期学校面向该领域的研究生，随后将举行会议，介绍前几周制定的主题的最新研究。目标是激励研究生探索数学不同领域之间的联系，超越他们在自己的研究生课程中可能看到的水平。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专业关系。我们注意到，许多以前在圣母大学数学中心学习的学生都获得了数学博士学位。交换代数及其与代数几何的相互作用课程的目标是教育本科生，并将对该领域感兴趣的研究人员聚集在一起。第一周将介绍有用的技术和适用于计算的例子。研究生暑期学校将使用Macaulay2项目介绍前沿主题和计算工具，会议将强调令人兴奋的新研究进展。关于p进l函数和特征变种的2020年计划的主题尚未完全确定，但将包括学生的交互式程序，以及高级主题，如Iwasawa主猜想，例外零猜想和特征变种。该计划的网站可访问www3.nd.edu/~cmnd/programs/https://centerformath.nd.edu/scientific-events-and-programs/This，该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The Center for Mathematics at the University of Notre Dame will run a 2019 program on Commutative Algebra and Its Interactions with Algebraic Geometry and a 2020 program on p-adic L-functions and Eigenvarieties. In 2019, the program will consist of an undergraduate summer school from May 28 to June 1, a graduate level summer school from June 3 to June 14, and an international research conference from June 16 to June 21. In 2020, the program will consist of a one week undergraduate summer school, a one week graduate level summer school, and a one week conference. The purpose of the programs is to introduce students at various levels to important ideas in commutative algebra and in number theory, which are both active and central areas of mathematics with many connections to other areas of mathematics and to science. The goal of the undergraduate 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 when they return to university. The graduate summer schools are geared towards graduate students in the field, and will be followed by a conference which will present current research on topics developed in the earlier weeks. The goal 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.The goal of the program Commutative Algebra and Its Interactions with Algebraic Geometry is to educate undergraduates and to bring together researchers interested in the area. The first week will introduce useful techniques and examples amenable to calculation. The graduate summer school will introduce cutting edge topics and computational tools using the Macaulay2 program, and the conference will emphasize exciting new research developments. The topics for the 2020 program on p-adic L-functions and Eigenvarieties are not completely set, but will include an interactive program for students, and advanced topics such as the Iwasawa main conjecture, the exceptional zero conjecture, and eigenvarieties.The program website is available at www3.nd.edu/~cmnd/programs/https://centerformath.nd.edu/scientific-events-and-programs/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.