Berkeley-Tokyo Summer School "Geometry, Representation Theory, and Mathematical Physics": On the Riemann-Hilbert correspondence

Seminar | August 25 | 1:15-2:45 p.m. | 375 LeConte Hall

 Andrea D'Agnolo, University of Padova

 Department of Mathematics

The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated categories of regular holonomic D-modules and of constructible sheaves. In a joint work with Masaki Kashiwara, we proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular. The construction of our target category is based on the theory of ind-sheaves by Kashiwara-Schapira and is influenced by Tamarkin’s work on symplectic topology. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Mochizuki and Kedlaya. I will survey this construction, sweeping under the carpet the most technical parts, and focusing on examples in dimension one.