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강연자 Masaki Kashiwara
소속 서울대학교/RIMS
date 2014-05-08
The original Riemann-Hilbert problem is to construct a liner ordinary differential equation with regular singularities whose solutions have  a given monodromy. Nowadays, it is formulated as a categorical equivalence of the category of regular holonomic D-modules and the category of perverse sheaves. It is a long standing problem to describe liner ordinary differential equations with irregular singularities in geometric terms.

Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived category of constructible sheaves with a full subcategory of ind-sheaves on the product of the base space and the real projective line. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Takuro Mochizuki and Kiran Kedlaya.

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List of Articles
카테고리 제목 소속 강연자
수학강연회 Recent progress on the Brascamp-Lieb inequality and applications file Saitama University Neal Bez
수학강연회 Connes's Embedding Conjecture and its equivalent file RIMS Narutaka Ozawa
수학강연회 Class field theory for 3-dimensional foliated dynamical systems file Kyushu University Morishita Masanori
수학강연회 Unprojection file University of Warwick / 서강대 Miles Reid
수학강연회 A new view of Fokker-Planck equations in finite and Infinite dimensional spaces file Bielefeld Univ./Purdue Univ. Michael Roeckner
수학강연회 Convex and non-convex optimization methods in image processing file Hong Kong Baptist University Michael Ng
수학강연회 Sheaf quantization of Hamiltonian isotopies and non-displacability problems file Kyoto Univ./서울대학교 Masaki Kashiwara
수학강연회 Codimension Three Conjecture file 교토대학교/서울대학교 Masaki Kashiwara
수학강연회 Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras file Kyoto University/서울대학교 Masaki Kashiwara
수학강연회 Riemann-Hilbert correspondence for irregular holonomic D-modules file 서울대학교/RIMS Masaki Kashiwara
수학강연회 The classification of fusion categories and operator algebras file Kyoto University Masaki Izumi
수학강연회 Conservation laws and differential geometry file Univ. of Wisconsin Marshall Slemrod
수학강연회 Quasi-homomorphisms into non-commutative groups file Kyoto Univ. Koji Fujiwara
수학강연회 Number theoretic results in a family file Univ. of Toronto / KIAS Kim, Henry
수학강연회 A-infinity functor and topological field theory file Simons Center for Geometry and Physics Kenji Fukaya
수학강연회 Deformation spaces of Kleinian groups and beyond file Osaka University Kenichi Ohshika
수학강연회 Analytic torsion and mirror symmetry file Kyoto University Ken-ichi Yoshikawa
수학강연회 Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields file Univ. Bremen Keivan Mallahi-Karai
수학강연회 Conformal field theory and noncommutative geometry file 동경대학교 Kawahigashi
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Harmonic Analysis (Kalachand Shuin) file BK21 Kalachand Shuin
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