RTG: Training Tomorrow's Workforce in Analysis and Applications

杜克大学的12名教师将带领博士后研究员、研究生和本科生参加一系列旨在提高研究技能和深化教育和培训经验的研究培训小组活动。包括暑期学校，本科研究会议，研讨会，专业发展活动和创新课程在内的活动将吸引广泛的学生和初级研究人员。本科生将欢迎早日到数学和数学研究的应用令人兴奋的世界。该项目将努力促进大学的数学专业，并将数学与实际应用联系起来，重点是招收处境不利的学生。研究生和博士后将受益于充满活力的研究氛围，创新的教学选择和专业发展研讨会。研究生将有机会获得行业实习，博士后研究员将获得指导研究生和本科生垂直整合研究项目的经验。这种深入的培训将通过广泛的现有成功的计划和旨在提高招聘，教育和研究的有效性的新举措来促进。RTG团队是一个在分析，概率，微分方程和计算数学方面相互联系的研究小组，包括经验丰富的高级教师，他们是各自领域的领导者，活跃的职业中期数学家和早期职业动态研究人员。在现代数学中，分析和概率工具和技术在广泛的方向上发挥着至关重要的作用。该项目的研究主题包括具有挑战性的分析问题（如克莱研究所关于Navier-Stokes方程的千年奖问题），以及现代应用（如图像处理，机器学习和生物建模）中产生的新应用分析和概率问题。除其他外，研究培训主题包括：流体动力学的PDE，奇点形成，随机强迫;逆问题和成像; PDE分析机器学习;复杂系统的建模和分析，并应用于生命科学;材料科学中的界面动力学和自由表面问题。RTG研究生和博士后学员将接触到重要研究方向的最新进展，他们将接受培训，将联合收割机尖端分析，概率，该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查进行评估来支持的搜索.

Twelve faculty members at Duke University will lead postdoctoral fellows, graduate students, and undergraduates in a collection of Research Training Group activities designed to enhance research skills and deepen educational and training experiences. Activities including summer schools, undergraduate research conferences, seminars, professional development events, and innovative courses will draw in a broad population of students and junior researchers. The undergraduate students will be welcomed early to the exciting world of applications of mathematics and mathematical research. The project will seek to promote the mathematics major at the University and connections of mathematics to practical applications, with a focus on recruitment of students of disadvantaged backgrounds. The graduate students and postdocs will benefit from a vibrant research atmosphere, innovative teaching options, and professional development workshops. Graduate students will have access to industry internships, and postdoctoral fellows will gain experience in mentoring graduate and undergraduate students in vertically integrated research projects. This in-depth training will be facilitated by a broad set of existing successful programs and by novel initiatives designed to raise effectiveness of recruitment, education, and research.The RTG team is an interconnected research group in Analysis, Probability, Differential Equations, and Computational Mathematics, including experienced senior faculty who are leaders in their fields, active mid-career mathematicians, and early career dynamic researchers. In modern mathematics, analytic and probabilistic tools and techniques play a crucial role in a broad range of directions. The research themes for this project include challenging analysis questions (such as the Clay Institute millennium prize problem on the Navier-Stokes equation), as well as new applied analysis and probabilistic questions arising from modern applications (such as image processing, machine learning, and biological modelling). Among others, research training themes include: PDE of fluid dynamics, singularity formation, stochastic forcing; inverse problems and imaging; PDE analysis for machine learning; modeling and analysis of complex systems, with applications to life sciences; interfacial dynamics and free surface problems in materials science. The RTG graduate students and postdoctoral trainees will be exposed to the most recent advances in important research directions, and they will be trained to combine cutting edge analytic, probabilistic, and computational tools with the intuition and broad expertise of an applied mathematician.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.