PECASE: Topics in Number Theory

该奖项为研究和教育项目提供资金，特别强调组合学和数论。拟研究配分函数的组合学、椭圆曲线的结构、模形式的傅里叶系数以及自同构l函数的特殊值。研究者希望进一步阐明椭圆曲线的莫德尔-韦尔群、数域的类群和塞尔默群的行为。除了他的研究之外，调查员还提出了一些基础广泛的活动，这些活动构成了促进各级教育的雄心勃勃和持续的努力。这包括在州立大学学区对当地有才华的高中生进行指导，以及在全国范围内与国家青年科学基金会合作举办年度研讨会。此外，研究者打算增加宾夕法尼亚州立大学的研究生和博士后在组合学和数论方面的工作机会。美国国家科学基金会强烈鼓励教师作为教育工作者和研究人员的早期发展。教师早期职业发展（CAREER）计划是一个基金会范围内的计划，为初级教师的整体职业发展提供支持。它将最广泛意义上的高质量研究和教育的支持与那些传统上在科学和工程领域代表性不足的人的充分参与结合在一个单一的项目中。该计划加强并强调了基金会对全面，平衡的学术生涯发展的重要性。

This award funds programs for research and education with specialemphasis in combinatorics and number theory. The investigatorplans to study the combinatorics of partition functions, thestructure of elliptic curves, the Fourier coefficientsof modular forms, and special values of automorphic L-functions.The investigator hopes to shed further light on the behaviorof Mordell-Weil groups of elliptic curves, class groups of numberfields, and Selmer groups. In addition to his research, the investigatorproposes a number of broadly based activities which constitutean ambitious and sustained effort for the promotion of education at all levels.This includes the mentoring of talented high school students locallywithin the State College School District, and nationally in theform of an annual workshop run in collaboration with theNational Youth Science Foundation. Moreover, the investigatorintends to enhance opportunities for graduate studentsand postdoctoral fellows working in combinatorics and number theoryat Penn State. The National Science Foundation strongly encourages the early developmentof academic faculty as both educators and researchers. The Faculty EarlyCareer Development (CAREER) Program is a Foundation-wide program thatprovides for the support of junior faculty within the context of theiroverall career development. It combines in a single program the support ofquality research and education in the broadest sense and the full participationof those traditionally underrepresented in sciences and engineering. Thisprogram enhances and emphasizes the importance the Foundation placeson the development of full, balanced academic careers.