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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 <2020년도 젊은 과학자상 수상 기념강연> Metastability of stochastic systems file 서울대학교 서인석
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Maximal averages in harmonic analysis file 서울대학교 이상혁
Math Colloquia From mirror symmetry to enumerative geometry file 서울대학교 오정석
Math Colloquia On classification of long-term dynamics for some critical PDEs file 서울대학교 김기현
Math Colloquia Homogeneous dynamics and its application to number theory file 서울대학교 임선희
Math Colloquia 학부생을 위한 강연: 브라질과 프랑스는 왜 축구를 잘 할까? - 경제와 수학과 축구와 법률 file 서울대학교 법과대학 김화진
BK21 FOUR Rookies Pitch 2021-2 Rookies Pitch: Probability Theory (조수빈) file 서울대학교 수리과학부 조수빈
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 Random matrices and operator algebras file 서울대학교 수학교육과 윤상균
BK21 FOUR Rookies Pitch 2021-2 Rookies Pitch: Stochastic Analysis (이해성) file 서울대학교 수학연구소 이해성
Math Colloquia <학부생을 위한 ɛ 강연> Mathematical Aspects of Machine Learning and Deep Learning AI file 서울대학교 컴퓨터공학부 장병탁
Math Colloquia Riemann-Hilbert correspondence for irregular holonomic D-modules file 서울대학교/RIMS Masaki Kashiwara
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Geometric Topology (김승원) file 성균관대학교 김승원
BK21 FOUR Rookies Pitch 2023-1 Number Theory (김민규) file 성균관대학교 김민규
Math Colloquia Toward bridging a connection between machine learning and applied mathematics file 성균관대학교 홍영준
Math Colloquia Lie group actions on symplectic manifolds file 성균관대학교 수학교육과 조윤형
Math Colloquia <학부생을 위한 ɛ 강연> Secure computation: Promise and challenges file 송용수 <학부생을 위한 ɛ 강연> Secure computation: Promise and challenges
BK21 FOUR Rookies Pitch 2021-1 Rookies Pitch: PDE, Dynamical Systems (박한솔) file 수리과학부 박한솔
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