Geometry Processing Summer Institute 2021

该奖项为为期6周的暑期几何学院（SGI）项目提供支持，该项目旨在通过与该学科顶尖研究人员的沉浸式互动，向广泛的学生介绍几何处理研究。该研究所将于2021年7月19日至8月28日在线举行；更多信息请访问其网站（http://geometry.institute）。总的来说，SGI的目标是：(1)激发学生和研究人员在几何处理方面的广泛合作；(2)启动涉及广泛资历的团队成员（本科生、研究生、教师、工业研究人员）的校际几何处理研究项目；(3)向学生介绍几何处理研究和开发；(4)使学生进入几何处理研究的“管道”多样化，不受性别、种族、社会经济背景和家庭院校的限制。该研究所的第一周将培训本科生和硕士学生的最先进的几何处理技术的参与者，旨在作为他们第一次接触这一学科。然后，在剩下的几周里，学生团队就研究问题进行合作，目标是探索高年级与会者建议的方向。除了这些为期一天的互动之外，参观者还将对边境地区进行演讲，并提供相关教程。参加六周的学生的机会成本将由研讨会支付。作为一门学科，几何处理提出了大量的理论挑战，这些挑战是由制造/制造、计算机视觉、物理模拟和高性能计算的实际考虑所激发的。参与者将接触并推进最先进的技术问题，从离散微分几何工具包的开发到形状处理管道中概率/不确定性的结合。参与几何处理研究也让数学专业的学生在一个更有形的环境中接触到微分几何等领域，再加上计算机可视化和具有直接影响的具体应用。我们的研讨会旨在在几何处理中的几个具体挑战上取得进展，包括鲁棒几何处理算法的开发，高通量形状分析方法的设计，基于微分/代数几何的理解和处理几何的合理机器学习架构的设计，以及从几何处理扩展到高维问题的机械。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 provides support for a 6-week program titled the Summer Geometry Institute (SGI), a workshop intended to introduce a broad pool of students to geometry processing research through immersive interaction with top researchers in the discipline. The Institute will be held July 19-August 28, 2021 online; more information can be found on its website (http://geometry.institute). Overall, SGI aims to accomplish the following objectives: (1) spark wide collaboration among students and researchers in geometry processing, (2) launch inter-university research projects in geometry processing involving team members across broad levels of seniority (undergraduate, graduate, faculty, industrial researcher), (3) introduce students to geometry processing research and development, and (4) diversify the "pipeline" of students entering geometry processing research, in terms of gender, race, socioeconomic background, and home institution. The first week of the Institute will train undergraduate and MS student participants on state-of-the-art techniques in geometry processing, intended as their first exposure to this discipline. Then, for the remaining weeks, student teams collaborate on research problems, with the goal of exploring directions suggested by senior attendees. Beyond these day-long interactions, visitors will give talks on frontier areas and lead relevant tutorials. The opportunity cost for students taking six weeks to participate will be covered by the workshop. As a discipline, geometry processing presents substantial theoretical challenges motivated by practical considerations of manufacturing/fabrication, computer vision, physical simulation, and high-performance computing. Participants will be exposed to---and will advance state-of-the-art in---technical problems ranging from the development of a toolkit for discrete differential geometry to the incorporation of probability/uncertainty in the shape processing pipeline. Participating in geometry processing research also gives mathematics students exposure to fields like differential geometry in a more tangible environment, coupled with computer visualizations and concrete applications with immediate impact. Our workshop is designed to make progress on several concrete challenges in geometry processing, including development of robust geometry processing algorithms, design of high-throughput shape analysis methods, design of sensible machine learning architectures for understanding and processing geometry built on foundations from differential/algebraic geometry, and extending machinery from geometry processing to higher-dimensional problems.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.