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Extra Form
Lecturer Masaki Kashiwara
Dept. 서울대학교/RIMS
date May 08, 2014
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.

Atachment
Attachment '1'
List of Articles
Category Subject Dept. Lecturer
Math Colloquia Contact topology of singularities and symplectic fillings file 순천대학교 권명기
Math Colloquia <학부생을 위한 ɛ 강연> Secure computation: Promise and challenges file 송용수 <학부생을 위한 ɛ 강연> Secure computation: Promise and challenges
Math Colloquia Lie group actions on symplectic manifolds file 성균관대학교 수학교육과 조윤형
Math Colloquia Toward bridging a connection between machine learning and applied mathematics file 성균관대학교 홍영준
Math Colloquia Riemann-Hilbert correspondence for irregular holonomic D-modules file 서울대학교/RIMS Masaki Kashiwara
Math Colloquia <학부생을 위한 ɛ 강연> Mathematical Aspects of Machine Learning and Deep Learning AI file 서울대학교 컴퓨터공학부 장병탁
Math Colloquia Random matrices and operator algebras file 서울대학교 수학교육과 윤상균
Math Colloquia <청암상 수상 기념 특별강연> 동형암호, 기계학습, 근사정수론 file 서울대학교 수리과학부 천정희
Math Colloquia <정년퇴임 기념강연> 수학의 시대정신(?) file 서울대학교 수리과학부 김명환
Math Colloquia 학부생을 위한 강연: 브라질과 프랑스는 왜 축구를 잘 할까? - 경제와 수학과 축구와 법률 file 서울대학교 법과대학 김화진
Math Colloquia Gaussian free field and conformal field theory file 서울대학교 강남규
Math Colloquia 학부생을 위한 강연: Introduction to partial differential equations file 서울대학교 변순식
Math Colloquia 곡선의 정의란 무엇인가? file 서울대학교 김영훈
Math Colloquia Fano manifolds of Calabi-Yau Type file 서울대학교 Atanas Iliev
Math Colloquia 젊은과학자상 수상기념강연: From particle to kinetic and hydrodynamic descriptions to flocking and synchronization file 서울대학교 하승열
Math Colloquia Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry file 서울대학교 Raphael Ponge
Math Colloquia 정년퇴임 기념강연회: 숙제 file 서울대학교 지동표
Math Colloquia Randomness of prime numbers file 서울대학교 임선희
Math Colloquia Non-commutative Lp-spaces and analysis on quantum spaces file 서울대학교 이훈희
Math Colloquia 학부생을 위한 ε 강연회: Sir Isaac Newton and scientific computing file 서울대학교 신동우
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