Special Seminar

Speaker: Giovanni Morando (University of Padova/RIMS)
Title: The Riemann-Hilbert correspondences and sheaves on subanalytic sites
Date (JST): Wed, Mar 07, 2012, 13:30 - 15:00
Place: Balcony B
Abstract: In the first part of this talk we will recall the Riemann-Hilbert correspondences: the regular one, the local irregular one on curves and the recent results by C. Sabbah, T. Mochizuki and K. Kedlaya in the general irregular case. In particular we will recall the classical procedure for the irregular case which consists first in giving a
formal decomposition of a flat meromorphic connection and then in finding a sectorial asymptotic lift of it.
In the second part of this talk, we will introduce the subanalytic site and the sheaf of tempered holomorphic functions. By means of easy examples we will explain their usefulness in the formal classification. We will point out the improvements achieved with these tools with respect to the classical ones. Further, we will discuss some results obtained on the constructibility of tempered solutions of holonomic D-modules which was conjectured in 2003 by M. Kashiwara and P. Schapira.