Connections between curves automorphic forms and L-functions: Particiapant support

Connections between curves automorphic forms and L-functions: Particiapant support Connections between curves, automorphic forms, and L-functions PROJECT SUMMARY Overview: Page A We request funding for a conference in number theory, specifically on connections between curves, modular forms, and L-functions. Each morning features a pair of plenary talks on recent research, and afternoons are devoted to collaborative work by the participants. The event is to be held at Arizona State University. Some of the top number theorists in these areas have agreed to participate, and Arizona State University has agreed to provide infrastructural support. Intellectual Merit : The conference will present lectures on recent developments in number theory and bring together experts on related topics in a workshop atmosphere. Areas of focus for the conference are hyperelliptic curves over the rationals, elliptic curves over low degree number fields, Hilbert modular forms, Siegel modular forms, and in all cases, corresponding L-functions. These are broad topics; we will pay particular attention to computational questions such as explicit examples which may be proven complete for some criteria. Broader Impacts : We are committed to having participants from all career stages, as well as having substantial participation by mathematicians from underrepresented groups. For graduate students, postdoctoral fellows, and junior faculty, the conference can serve as a springboard for their future in the profession. Computational results presented or worked on at the conference will be incorporated into the L-functions and Modular Forms Database, an publicly available web site which is the result of an international collaboration of many number theorists. The site provides data which is useful for mathematical research, and serves as an educational tool helping both young and experienced number theorists see some of the objects and subtle relationships which are an important part of modern number theory.