RTG: Analysis of Partial Differential Equations

该项目的目标是在几个方向上加强德克萨斯大学奥斯汀分校偏微分方程（PDE）分析领域的研究培训活动。 偏微分方程的分析是数学的一个领域，对自然科学的发展至关重要。事实上，PDE被用于许多现象的建模，如物质的原子性质，天体的动力学，流体和气体的力学（例如用于天气预报），以及电磁现象的研究（现代通信的基础）。 这种应用的多样性反映在一个领域的复杂性，丰富的开放问题和富有成效的研究方向。因此，对研究生和本科生进行分析培训对美国的科学和经济竞争力至关重要，任何吸引学生到该地区的努力也是如此。与此同时，要引导学生形成一种不只是技术性的、过于专业化的学科观，而且要成功地强调该领域的多功能性和深度，就需要一个团队的协调工作。（以色列，Maggi，Patrizi，Pavlovic，Vasseur），以及UT Austin的PDE专家组（包括Beckner，Caffarelli，Chen，Gamba和Ren），坚定地致力于研究培训，其联合研究活动涵盖了PDE中相互关联的主题的广阔领域，并获得了国际认可。该项目将包括5个博士后奖学金和20个年度研究生奖学金，从而增加了在UT奥斯汀PDE分析培训的美国公民的数量;以及一系列全面的行动，旨在提高我们的活动在本科生中的可见度，包括内部和外部UT奥斯汀，并特别强调来自德克萨斯州中部大学的学生服务于大量少数民族人口。小组的教育活动（研讨会、课程、非正式讲座、阅读课程等）将仔细重新审视和加强，让学员接触新的想法，并增加辅导，教学，专业发展和各级互动的机会。一个年度暑期课程和一个专业设计和维护的网站将增加我们的计划的全国知名度，并帮助分散其最成功的做法。最终预期的结果是在我们部门和其他部门的研究培训文化中创造积极持久的变化。该奖项反映了NSF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 goal of this project is enhancing in several directions the research-training activities in the area of the Analysis of partial differential equations (PDE) at the University of Texas (UT) at Austin. The Analysis of PDE is an area of Mathematics that is central to the development of Natural Sciences. Indeed, PDE are used in the modeling of many phenomena, like the atomic properties of matter, the dynamics of celestial bodies, the mechanics of fluids and gases (used for example in weather forecast), and the study of electromagnetic phenomena (fundamental to modern communications). This variety of applications is reflected in the complexity of a field rich in open problems and fruitful research directions. The training of graduate and undergraduate students in Analysis is thus crucial to the scientific and economic competitiveness of the US, and so is any effort to attract students to the area. At the same time, leading students to achieve a view of the subject that is not merely technical and overly specialized, but also succeeds in emphasizing the versatility and depth of the field, requires the coordinated work of a group.The five co-PIs (Israel, Maggi, Patrizi, Pavlovic, Vasseur), together with the larger group of PDE experts at UT Austin (including Beckner, Caffarelli, Chen, Gamba and Ren), are strongly committed to research training, with a combined research activity that covers a vast area of interconnected topics in PDE, and has received international recognition. This project will include 5 postdoctoral fellowships and 20 annual graduate fellowships, thus increasing the number of US citizens trained in the Analysis of PDE at UT Austin; and a comprehensive series of actions aimed at increasing the visibility of our activities among undergraduate students, both internally and externally to UT Austin, and with particular emphasis on students from universities in Central Texas serving large minority populations. The educational activities of the group (seminars, courses, informal lectures, reading courses, etc.) will be carefully revisited and enhanced, to expose trainees to new ideas, and to multiply the opportunities for mentoring, teaching, professional development, and interactions at all levels. An annual Summer Program and a professionally designed and maintained website will increase the national visibility of our program and help dispersing its most successful practices. The ultimate expected outcome is creating positive lasting changes in the research training culture at our department and beyond.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.