Second RIMS-UCI Collaboration Conference: Arithmetic Applications of Moduli Degeneration; May 7-10, 2003; Irvine, CA

University Of California-Irvine, Irvine CA

Investigators

Abstract

Title: RIMS-UCI Collaboration Conference on Arithmetic Applications of Moduli Degeneration This project supports US participants to attend a workshop at UC Irvine, May 7 to May 10, 2003. The lectures combine algebra and complex analytic geometry to give new insights into collections of algebraic relations from refined parameter (moduli) spaces. Some lectures introduce a new zoo of cusp types. These generalize cusps attached to modular curves. They extract what governs previously subtle problems and enhance mature topics like Deligne's tangential base points and Belyi covers. Tempered fundamental groups, Modular Towers and cusp embeddings of curves in their jacobians appear in featured lectures. Number theorists and algebraic geometers will find results going far beyond those from a previous workshop in Kyoto, October, 2002 at RIMS Institute. Especially, there are new applications to motivate students and post-doctorals to learn techniques for classifying algebraic equations from their bad reduction types. The invited speakers, and a capstone volume to the previous publication series, will attract new Ph.D. students. This project supports US participants to attend a workshop at UC Irvine, May 7 to May 10, 2003. Mathematical objects described by equations can be painfully complicated, full of peripheral data one would like to eliminate. Special structures on parameter spaces for these objects can help researchers filter all but the essentials from these equations. This workshop follows the more technical workshop at RIMS Institute in Kyoto, October, 2002. Our speakers will emphasize significant new contributions to this data filtering process based on cusp geometry. A lecture series by Yves Andre and focused lectures by the other invited speakers will attract new Ph.D. students to the field. They will learn new ideas for classifying equations by their bad reduction types. Applications will be to a wide range of topics, including string theory and height measures. A conference proceedings will disseminate the results in a capstone to a previous series of related publications.