Colloquium: "Riemann-Hilbert correspondence from logarithmic and relative perspectives"

Abstract: Riemann-Hilbert correspondence plays an important role in modern geometry. Roughly speaking, it establishes connections among geometry, topology and algebra. In 1981, Kashiwara and Mebkhout proved Riemann-Hilbert correspondence for regular holonomic D-modules, which gave an answer to Hilbert's 21st problem. My research explores Riemann-Hilbert correspondence from both logarithmic and relative perspectives. In this talk, I will give an overview of the recent progress in this direction. More precisely, I will discuss Riemann-Hilbert correspondence on smooth log pairs by using logarithmic D-modules and a relative version of Riemann-Hilbert correspondence by using Bernstein-Sato polynomials/ideals. As an application, I will also discuss index formulas for non-compact smooth varieties.

Host: Matt Kerr