RTG: Frontiers in Applied Analysis

RTG：应用分析前沿

• 批准号: 2342349
• 负责人: Dejan Slepcev
• 金额: $ 246.2万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-09-01 至 2029-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2342349&HistoricalAwards=false
• 关键词: RTG; Frontiers; Applied; Analysis

The increased use of sophisticated mathematical models in applied fields calls for a mathematical workforce with a strong theoretical foundation and a clear vision of how concepts of analysis can be applied to meet challenges at the frontiers of science and technology. The research and training of this RTG focuses on applied analysis, which encompasses partial differential equations, calculus of variations, geometric analysis, stochastic analysis, numerical analysis, optimal transportation, and their applications to relevant models in materials science, geometry processing, and machine learning. This RTG will create a rich ecosystem of activities that is attentive to the needs of trainees at each level. Undergraduate students will be introduced to research in applied analysis and will work alongside graduate students and faculty in innovative course-based undergraduate research and intense summer undergraduate research programs. An undergraduate research conference will provide a venue for presentations, networking, and learning about career opportunities in applied mathematics. This RTG will provide comprehensive mentorship for graduate students and postdocs in a stimulating environment with topics courses, weekly working groups, seminars (including a new seminar series focused on uses of applied analysis across disciplines), workshops, and summer schools. The training will be enhanced by regular professional development activities and visits to international partners from leading research groups in Europe. Particular attention will be given to recruiting and ensuring the success of trainees from underrepresented groups. Overall, the RTG will help attract students to applied mathematics, and will create a technically trained US workforce with expertise in advanced tools of applied analysis ready to engage with future challenges that arise in applied disciplines.Scientifically, the RTG will spark collaborative efforts to address compelling problems in applied analysis; in particular, variational problems for novel materials, geometric structures in minimization problems, new descriptions of geometry processing tasks, quantitative study of mixing and enhanced dissipation, innovative geometries and gradient flows allowing for accurate computation in high dimensions, and modeling and simulation of problems involving thermomechanics. These collaborations will bridge disciplines, and lead to the creation of new mathematics necessary to address applied challenges.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.

在应用领域中，越来越多的数学模型的使用越来越多地要求建立一个数学劳动力，并具有强大的理论基础，并清楚地看出了如何应用分析概念来应对科学和技术领域的挑战。该RTG的研究和培训集中在应用分析上，其中包括部分微分方程，变化的计算，几何分析，随机分析，数值分析，最佳运输，最佳运输及其在材料科学，几何学处理和机器学习中的相关模型中的应用。该RTG将创建一个丰富的活动生态系统，这些活动对每个级别的受训者的需求都很关注。本科生将被介绍进行应用分析研究，并将与研究生和教职员工一起从事创新课程的本科研究和激烈的夏季本科研究计划。一项本科研究会议将为演讲，网络和了解应用数学的职业机会提供一个场所。该RTG将在刺激性的环境中为研究生和博士后提供全面的指导，其中包括主题课程，每周工作组，研讨会（包括新的研讨会系列，重点介绍跨学科的应用分析），研讨会和暑期学校。定期的专业发展活动和访问欧洲领先的研究小组的国际合作伙伴将增强培训。特别关注招募和确保来自代表性不足的群体的学员成功。总体而言，RTG将有助于吸引学生进行应用数学，并将创建一个经过技术培训的美国劳动力，并在高级应用分析工具方面具有专业知识，准备应对应用学科中出现的未来挑战。SCIENT，RTG将引发协作性的努力，以解决应用分析中令人信服的问题；特别是，新型材料的各种问题，最小化问题中的几何结构，几何处理任务的新描述，混合和增强耗散的定量研究，创新的几何形状以及梯度流以及允许在高维度中进行准确计算以及涉及热力学问题的问题的准确计算。这些合作将弥合学科，并导致创建应对应用挑战所必需的新数学。该奖项反映了NSF的法定使命，并使用基金会的知识分子优点和更广泛的影响评估标准，认为值得通过评估来获得支持。