Summer School in Computational Number Theory 2019

该奖项支持参加一系列计算数论暑期学校。即将到来的暑期学校将于2019年夏天在北卡罗来纳大学格林斯博罗分校举行，我们将以建筑为主题。为期一周的暑期学校的目的是通过让研究生接触到数论中许多对象的建设性和计算方法来补充传统的培训。这进一步加深了他们的知识，并为学生的研究提供了额外的工具。此外，学校为学生提供了与该领域专家密切合作的机会。与p进约化群相关的Bruhat-Tits构造是与半简单李群相关的经典对称空间的简单类比。对这些结构的研究是理解p进群和算术格的重要工具。建筑在数论、几何、代数和组合学等多个领域发挥着重要作用。暑期学校对学生的研究生涯和博士后生活都很有价值，因为这个活动有助于创建研究社区。通过与各自领域的其他研究生会面和合作，学生们为未来的合作奠定了基础。在暑期学校结束后的几年里，他们将有机会在一个地区会议上再次见面，包括棕榈数论系列会议和东南数字会议。此外，通过向学生介绍数论的计算方法，该项目将提高下一代数学家在研究中使用计算技术的能力。欲了解更多信息，请参阅http://www.uncg.edu/math/numbertheory/summerschool/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。

This award supports participation in a series of summer schools in computational number theory. The upcoming summer school, to be held at the University of North Carolina - Greensboro, summer 2019 we be on the topic of Buildings. The aim of the one-week summer school is to complement the traditional training that graduate students receive by exposing them to a constructive and computational approach to many objects in number theory. This furthers their knowledge and gives the students additional tools for their research. Furthermore, the school provides the students the opportunity to work closely with experts in the field.The Bruhat-Tits building associated to a p-adic reductive group is a simplicial analogue of the classical symmetric space associated to a semi-simple Lie group. The study of these buildings has been an important tool in understanding p-adic groups as well as arithmetic lattices. Buildings have enjoyed playing key roles in several areas, including number theory, geometry, algebra, and combinatorics. The summer school is valuable to students for their careers as researchers and in their post-doctoral lives, since the event helps to create research communities. By meeting and working with other graduate students in their field, the students lay the foundation for future collaboration. In the years after the summer school, they will have opportunities to meet again at one of the regional conferences, including the Palmetto Number Theory Series and the South Eastern Meeting on Numbers. Additionally, by introducing the students to a computational approach to number theory, this project will enhance the next generation of mathematicians by increasing their ability to use computing technology in their research.For more information, see http://www.uncg.edu/math/numbertheory/summerschool/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.