This award funds programs for research and education with special emphasis in combinatorics and number theory. The investigator plans to study the combinatorics of partition functions, the structure of elliptic curves, the Fourier coefficients of modular forms, and special values of automorphic L-functions. The investigator hopes to shed further light on the behavior of Mordell-Weil groups of elliptic curves, class groups of number fields, and Selmer groups. In addition to his research, the investigator proposes a number of broadly based activities which constitute an ambitious and sustained effort for the promotion of education at all levels. This includes the mentoring of talented high school students locally within the State College School District, and nationally in the form of an annual workshop run in collaboration with the National Youth Science Foundation. Moreover, the investigator intends to enhance opportunities for graduate students and postdoctoral fellows working in combinatorics and number theory at Penn State.
The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation-wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in sciences and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers.
