1차원 공간상의 움직임으로 6n차원의 공간구조를 이해하는 방법론 제시This study is related to the structure of moduli space which is the space of all the geometric shapes that a surface can have. Moduli space is high-dimensional, and it is difficult to directly understand such a high-dimensional space. The best way to understand a given space is to break up the given space into subspaces of lower dimensions and build up an understanding of the entire space from lower levels of understanding. Surprisingly, splitting n-dimensional space into n-1-dimensional space is related to the dynamics of one-dimensional space. In this study, we found the complete answer to the differential possibility of the one-dimensional dynamics related to the moduli space, and presented a methodology to understand the 6n-dimensional moduli space.

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dc.contributor.author백형렬-
dc.date.accessioned2021-01-29T04:31:00Z-
dc.date.available2021-01-29T04:31:00Z-
dc.date.issued2019-
dc.identifier.urihttp://hdl.handle.net/10203/280379-
dc.identifier.urihttps://archives.kaist.ac.kr/research.jsp?year=2019&view=view02-
dc.identifier.urihttps://archives.kaist.ac.kr/eng/research.jsp?year=2019&view=view02-
dc.descriptionKAIST 2019 대표 연구성과 10선-
dc.description.abstract본 연구는 곡면이 가질 수 있는 모든 기하적인 형태들을 모아놓은 공간인 모듈라이 공간의 구조와 관련되어 있다. 모듈라이 공간은 고차원 공간으로, 이렇게 차원이 높은 공간을 직접 이해하기는 어렵다. 주어진 공간을 이해하는 가장 좋은 방법은 주어진 공간을 더 낮은 차원의 부분공간들로 쪼개어 낮은 차원의 이해로부터 전체 공간의 이해를 구축해나가는 것이다. 신기하게도 n차원 공간을 n-1차원 공간으로 쪼개어 보는 것은 1차원 공간상의 동역학계와 관계가 있다. 본 연구에서는 모듈라이 공간과 관련된 1차원 동역학계의 미분가능성에 대한 완전한 답을 찾았고, 그로부터 6n차원의 모듈라이 공간을 이해할 수 있는 방법론을 제시했다.-
dc.languagekor-
dc.publisher한국과학기술원-
dc.title1차원 공간상의 움직임으로 6n차원의 공간구조를 이해하는 방법론 제시-
dc.title.alternativeThis study is related to the structure of moduli space which is the space of all the geometric shapes that a surface can have. Moduli space is high-dimensional, and it is difficult to directly understand such a high-dimensional space. The best way to understand a given space is to break up the given space into subspaces of lower dimensions and build up an understanding of the entire space from lower levels of understanding. Surprisingly, splitting n-dimensional space into n-1-dimensional space is related to the dynamics of one-dimensional space. In this study, we found the complete answer to the differential possibility of the one-dimensional dynamics related to the moduli space, and presented a methodology to understand the 6n-dimensional moduli space.-
dc.typeReport-
dc.description.alternativeAbstractThis study is related to the structure of moduli space which is the space of all the geometric shapes that a surface can have. Moduli space is high-dimensional, and it is difficult to directly understand such a high-dimensional space. The best way to understand a given space is to break up the given space into subspaces of lower dimensions and build up an understanding of the entire space from lower levels of understanding. Surprisingly, splitting n-dimensional space into n-1-dimensional space is related to the dynamics of one-dimensional space. In this study, we found the complete answer to the differential possibility of the one-dimensional dynamics related to the moduli space, and presented a methodology to understand the 6n-dimensional moduli space.-
dc.description.department한국과학기술원 : 수리과학과-
dc.contributor.localauthor백형렬-
dc.contributor.alternativeauthorHyungryul Baik-

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