RTG: Analysis of Partial Differential Equations

点击翻译按钮获取中文摘要

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.