Speaker: Kiran Kedlaya (UCSD)

Time: Dec 26, 2012 14:00 - 16:30

Title: Formal classification of differential equations and Berkovich spaces

Abstract:
The formal classification of modules with connection is important in the theory of ordinary differential equations with meromorphic coefficients, for instance because of its role in the study of asymptotic behavior of solutions near a singularity. We'll review this classification (the Turrittin decomposition theorem), then discuss a higher-dimensional analogue. The new feature in the higher-dimensional case is that one must first make some blowups before the classification can take effect, and the difficulty is to establish a finiteness property for these blowups. This is done using the study of integrable connections on Berkovich analytic spaces, and primarily for Berkovich curves where the study is mostly of a combinatorial nature.

Location: Room 82J12, Building Jiayibing, BICMR (北京国际数学研究中心 82号甲乙丙楼82J12教室)