RTG: Analysis and Partial Differential Equations at the University of Wisconsin

这个研究训练小组项目将新的学生和博士后研究人员带入分析和偏微分方程的研究小组。12名高级人员将招募初级数学家作为学生和博士后加入小组，并在整个培训过程中密切指导他们。该项目特别强调通过扩大、有针对性的招聘工作和结构化的指导，使集团的本科和研究生课程多样化。研讨会交流和国际合作将在研究小组之间建立导师联盟，同时也为其他机构的高级研究生和博士后研究人员提供机会来威斯康星大学麦迪逊分校与该小组的高级人员进行互动。年度RTG研讨会将为所有级别的研究人员之间分享研究成果和发展合作关系提供更密集的场所。在学年期间，每周的研究生写作小组将由来自其他大学的早期职业研究人员参加的年度写作营来补充。该项目利用威斯康星大学麦迪逊分校教师在分析和偏微分方程方面的经验，将各级经验的数学家与前沿研究联系起来。该项目为受训者提供了在谐波分析、谱理论、解析数论、色散方程、流体动力学以及非线性椭圆和抛物方程等快速发展领域成为领导者所需的机会和指导。传统的研究生和博士后研究机会将通过以社区为导向的指导结构来增加，而新的本科研究项目和课程将为最年轻的受训者提供在高需求研究领域的立足点。纵向整合，即高级人员、博士后研究人员、研究生和本科生在项目上合作，将提高研究效率，同时也为受训者提供机会，发展他们作为下一代教育工作者和导师的技能。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 Research Training Group project brings new students and postdoctoral researchers into research groups in analysis and partial differential equations. The twelve senior personnel will recruit junior mathematicians to join the group as students and postdocs and closely mentor them throughout their training. The project places particular emphasis on diversifying the group’s undergraduate and graduate programs through expanded, targeted recruitment efforts and structured mentoring. Seminar exchanges and international collaborations will develop a mentor coalition among research groups, while also providing advanced graduate students and postdoctoral researchers at other institutions opportunities to come to the University of Wisconsin-Madison to interact with the group’s senior personnel. Annual RTG workshops will provide a more intensive venue for the sharing of research results and development of collaborative relationships among researchers from all seniority levels. Weekly graduate writing groups during the academic year will be complemented by annual writing camps involving early-career researchers from other universities.The project capitalizes on the experience of the University of Wisconsin-Madison faculty in analysis and partial differential equations to connect mathematicians at all levels of experience with cutting edge research. The project gives trainees the opportunities and mentoring needed to become leaders in the rapidly growing fields of harmonic analysis, spectral theory, analytic number theory, dispersive equations, fluid dynamics, and nonlinear elliptic and parabolic equations. Traditional graduate and postdoctoral research opportunities will be augmented by community-oriented mentoring structures, while new undergraduate research programs and courses will provide the most junior trainees a foothold in high-demand research areas. Vertical integration, in which senior personnel, postdoctoral researchers, and graduate and undergraduate students collaborate on projects, will increase research productivity while also providing opportunities for trainees to develop their skills as the next generation of educators and mentors.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.