https://www.math.snu.ac.kr/board/files/attach/images/701/ff97c54e6e21a4ae39315f9a12b27314.png
Extra Form
Lecturer 박종일
Dept. 서울대학교
date Sep 26, 2013
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
Attachment '1'
List of Articles
Category Subject Dept. Lecturer
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 정년퇴임 기념강연회: 숙제 file 서울대학교 지동표
Math Colloquia Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry file 서울대학교 Raphael Ponge
Math Colloquia 학부생을 위한 ε 강연회: Sir Isaac Newton and scientific computing file 서울대학교 신동우
Special Colloquia A New Approach to Discrete Logarithm with Auxiliary Inputs file 서울대학교 천정희
Math Colloquia 정년퇴임 기념강연: Volume Conjecture file 서울대학교 김혁
Special Colloquia Irreducible Plane Curve Singularities file 서울대학교 강정혁
Math Colloquia Subgroups of Mapping Class Groups file 서울대학교 김상현
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: Mathematics from the theory of entanglement file 서울대학교 계승혁
Math Colloquia Brownian motion and energy minimizing measure in negative curvature file 서울대학교 임선희
Math Colloquia Combinatorial Laplacians on Acyclic Complexes file 서울대학교 국웅
Special Colloquia Contact topology and the three-body problem file 서울대학교 Otto van Koert
Math Colloquia Fefferman's program and Green functions in conformal geometry file 서울대학교 Raphaël Ponge
Special Colloquia 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds file 서울대학교 박종일
Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Next
/ 15