PECASE: Topics in Number Theory

该奖项用于研究和教育项目，重点是组合学和数论。作者计划研究配分函数的组合、椭圆曲线的结构、模形式的傅立叶系数和自同构L函数的特殊值，希望进一步阐明椭圆曲线的Mordell-Weil群、数域的类群和Selmer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，其中包括在州立大学学区内指导有才华的高中生，并以与国家青年科学基金会合作举办的年度研讨会的形式在全国范围内指导有才华的高中生。此外，研究人员打算增加宾夕法尼亚州立大学从事组合学和数论工作的研究生和博士后研究员的机会。国家科学基金会强烈鼓励早期发展作为教育工作者和研究人员的学术人员。学院早期职业发展(Career)计划是一个全基金会范围的计划，在他们整体职业发展的背景下为初级教师提供支持。它结合了对最广泛意义上的高质量研究和教育的支持，以及那些在科学和工程领域传统上代表性较低的人的充分参与。这项计划加强并强调了基金会对充分、平衡的学术事业发展的重要性。

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.