On the Riemann-Hilbert correspondence II
speaker: Andrea D'Agnolo (Università di Padova)abstract: Hilbert's twenty-first problem (a.k.a. Riemann-Hilbert problem) asks for the existence of linear ordinary differential equations with prescribed regular singularities and monodromy. In higher dimensions, Deligne formulated it as a correspondence between regular meromorphic flat connections and local systems. In the early eighties, Kashiwara generalized it to a correspondence between regular holonomic D-modules and perverse sheaves on a complex manifold. The analogous problem for possibly irregular holonomic D-modules (a.k.a. the Riemann–Hilbert–Birkhoff problem) has been standing for a long time. One of the difficulties was to find a substitute target to the category of perverse sheaves. In the 80's, Deligne and Malgrange proposed a correspondence between meromorphic connections and Stokes filtered local systems on a complex curve. Recently, Kashiwara and the speaker solved the problem for general holonomic D-modules in any dimension. The construction of the target category is based on the theory of ind-sheaves by Kashiwara-Schapira and uses Tamarkin’s work on symplectic topology. Among the main ingredients of the proof is the description of the structure of flat meromorphic connections due to Mochizuki and Kedlaya.
timetable:
Sun 4 Nov, 11:00 - 12:00, Sala Conferenze Centro De Giorgi
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