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Extra Form
강연자 박종일
소속 서울대학교
date 2013-09-26
Despite of the fact that 4-dimensional manifolds together with 3-dimensional manifolds are the most fundamental and important objects in geometry and topology and topologists had great achievements in 1960's, there has been little known on 4-manifolds, in particular on smooth and symplectic 4-manifolds, until 1982. In 1982, M. Freedman classified completely simply connected topological 4-manifolds using intersection forms and S. Donaldson introduced gauge theory to show that some topological 4-manifolds do not admit a smooth structure. Since then, there has been a great progress in smooth and symplectic 4-manifolds mainly due to Donaldson invariants, Seiberg-Witten invariants and Gromov-Witten invariants. But the complete understanding of 4-manifolds is far from reach, and it is still one of the most active research areas in geometry and topology.
My main research interest in this area is the geography problems of simply connected closed smooth (symplectic, complex) 4-manifolds. The classical invariants of a simply connected closed 4-manifold are encoded by its intersection form , a unimodular symmetric bilinear pairing on H2(X : Z). M. Freedman proved that a simply connected closed 4-manifold is determined up to homeomorphism by . But it turned out that the situation is strikingly different in the smooth (symplectic, complex) category mainly due to S. Donaldson. That is, it has been known that only some unimodular symmetric bilinear integral forms are realized as the intersection form of a simply connected smooth (symplectic, complex) 4-manifold, and there are many examples of infinite classes of distinct simply connected smooth (symplectic, complex) 4-manifolds which are mutually homeomorphic. Hence it is a fundamental question in the study of 4-manifolds to determine which unimodular symmetric bilinear integral forms are realized as the intersection form of a simply connected smooth (symplectic, complex) 4-manifold - called a existence problem, and how many distinct smooth (symplectic, complex) structures exist on it - called a uniqueness problem. Geometers and topologists call these ‘geography problems of 4-manifolds’.
Since I got a Ph. D. with a thesis, Seiberg-Witten invariants of rational blow-downs and geography problems of irreducible 4-manifolds, I have contributed to the study of 4-manifolds by publishing about 30 papers - most of them are average as usual and a few of them are major breakthrough for the development of 4-manifolds theory. In this talk, I'd like to survey what I have done, what I have been doing and what I want to do in near future.
Atachment
첨부 '1'
List of Articles
카테고리 제목 소속 강연자
수학강연회 Theory and applications of partial differential equations file 서울대 변순식
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Probability Theory (변성수) file KIAS 변성수
수학강연회 1 is big enough to understand 3 file 카이스트 백형렬
수학강연회 Essential dimension of simple algebras file KAIST 백상훈
수학강연회 <학부생을 위한 ɛ 강연> Introduction to the incompressible Navier-Stokes equations file UNIST 배한택
수학강연회 Mixed type PDEs and compressible flow file POSTECH 배명진
수학강연회 Seoul ICM 2014 유치과정 개요 및 준비전략 file 포항공과대학교 박형주
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Algebraic Geometry (박현준) file KIAS 박현준
BK21 FOUR Rookies Pitch 2021-1 Rookies Pitch: PDE, Dynamical Systems (박한솔) file 수리과학부 박한솔
BK21 FOUR Rookies Pitch 2021-1 Rookies Pitch: PDE, Regularity Theory (박진완) file 수학연구소 박진완
수학강연회 Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds file KIAS 박진성
수학강연회 Iwasawa main conjecture and p-adic L-functions file 포항공과대학교 박지훈
특별강연 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds file 서울대학교 박종일
수학강연회 Restriction theorems for real and complex curves file 포항공과대학교 박종국
수학강연회 Infinite order rationally slice knots file 카이스트 수리과학과 박정환
수학강연회 Hybrid discontinuous Galerkin methods in computational science and engineering file 연세대 박은재
수학강연회 How to solve linear systems in practice file 이화여대 수학과 민조홍
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Symplectic Topology (문지연) file 수학연구소 문지연
수학강연회 Generalized multiscale HDG (hybridizable discontinuous Galerkin) methods for flows in highly heterogeneous porous media file 육군사관학교 문미남
수학강연회 WGAN with an Infinitely wide generator has no spurious stationary points file 서울대학교 류경석
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