Researchers Database
MURAI Hiroko
| ■Faculty | Faculty Division of Natural Sciences Research Group of Mathematics | |||
| ■Position | Associate Professor | |||
Last Updated :2024/04/15
researchmap
Profile and Settings
Name (Japanese)
MuraiName (Kana)
Hiroko
Research Interests
Research Areas
Research Experience
- 2009, 2012, :国立大学法人奈良女子大学 理学部
- 2009, 2012, :Faculty of Science,Nara Women'sUniversity
- 2012, -:国立大学法人奈良女子大学 研究院 自然科学系 数学領域
- 2012, -:Faculty of Science,Nara Women'sUniversity
- 2008, 2009, :東京電機大学情報環境学部
- 2008, 2009, :Tokyo Denki University School of Information Environment
- 助教
- Assistant Professor
Education
- 2007, Nara Women's University, 人間文化研究科, Japan
- 2007, Nara Women's University, Graduate School, Doctral Research Course in Human Culture
- 2002, Kyoto University, Faculty of Science, Japan
- 2002, Kyoto University, Faculty of Science
Association Memberships
Ⅱ．研究活動実績
Published Papers
- Not Refereed, Sep. 2022
- Refereed, 研究集会「結び目の数理II」報告集, 曲面上のグラフのKrushkal 多項式, 村井紘子; 山村瑠納, Dec. 2019, Scientific journal
- Refereed, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, WORLD SCIENTIFIC PUBL CO PTE LTD, A distance on the equivalence classes of spherical curves generated by deformations of type RI, Funakoshi, Yukari; Hashizume, Megumi; Ito, Noboru; Kobayashi, Tsuyoshi; Murai, Hiroko, In this paper, we introduce a distance (d) over bar (w)(3) on the equivalence classes of spherical curves under deformations of type RI and ambient isotopies. We obtain an inequality that estimate its lower bound (Theorem 1). In Theorem 2, we show that if for a pair of spherical curves P and P', (d) over bar (w)(3)([P],[P']) = 1 and P and P' satisfy a certain technical condition, then P' is obtained from P by a single weak RIII only. In Theorem 3, we show that if P and P' satisfy other conditions, then P' is ambient isotopic to a spherical curve that is obtained from P by a sequence of a particular local deformations, which realizes (d) over bar (w)(3)([P], [P'])., Oct. 2018, 27, 12, Scientific journal, 10.1142/S0218216518500669
- Refereed, Kobe Journal of Mathematics, Gap of codimension one foliations, MURAI Hiroko, 2012, 29, 1, 24, Scientific journal
- Refereed, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, WORLD SCIENTIFIC PUBL CO PTE LTD, Depths of the foliations on 3-manifolds each of which admits exactly one depth 0 leaf, Hiroko Murai, In [ 2], Cantwell-Conlon introduced a knot invariant, called depth. In this paper, we discuss the depth of a foliation F on a 3- manifold with F being (*) " codimension one, transversely oriented, taut, and proper". We show that for each n > 0, there exists a 3-manifold M such that ( minimal depth of F on M with F being (*) and having exactly one depth 0 leaf) is greater than ( minimal depth of F on M with F being (*)) + n., May 2007, 16, 5, 641, 669, Scientific journal, 10.1142/S0218216507005427
- Refereed, Proceedings of Intelligence of Low Dimensional Topology 2006, Series on Knots and Everything, Gap of the depths of leaves of foliations, MURAI Hiroko, 2007, 40, 223, 230, Scientific journal
- Kyoto-Math Preprint Series, Gap of Depths of Leaves on Codimension One Foliations, Hiroko MURAI, May 2007, 7
Presentations
- Oral presentation, 09 Nov. 2020, 11 Nov. 2020
- 研究集会「結び目の数学X」, Complexes induced from spherical curves and distances derived from them, 2017
- Complexes induced from spherical curves and distances derived from them, 2017
- Low dimensional topology and number theory VII, A construction of flat foldable origami via similarity structure, 2015
- Low dimensional topology and number theory VII, A construction of flat foldable origami via similarity structure, 2015
- The Seventh East Asian School of Knots and Related Topics, Toward Haken type theorems for essential laminations in 3-manifolds : Proposal for fundamental settings and applications, 2011
- Workshop on topology and geometry - Heegaard splitting of 3-manifolds -, A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces, 2011
- Workshop on low dimensional topology in Shanghai and Suzhou, A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces, 2011
- The Seventh East Asian School of Knots and Related Topics, Toward Haken type theorems for essential laminations in 3-manifolds : Proposal for fundamental settings and applications, 2011
- Workshop on topology and geometry - Heegaard splitting of 3-manifolds -, A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces, 2011
- Workshop on low dimensional topology in Shanghai and Suzhou, A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces, 2011
- E-KOOK Seminar 2010, Toward Haken type theorems for essential laminations in 3-manifolds : Proposal for fundamental settings and applications, 2010
- E-KOOK Seminar 2010, 3-manifolds : Proposal for fundamental settings and applications, 2010
- 村井紘子; 山村瑠納, 結び目の数理II, 曲面上のグラフのKrushkal多項式について, Oral presentation, 20 Dec. 2019, 18 Dec. 2019, 21 Dec. 2019
- Hiroko Murai; Reika Yamamoto, 日本応用数理学会2022年度年会, On the existence of cylinder solutions of waterbomb tessellation, Oral presentation, 08 Sep. 2022, 08 Sep. 2022, 10 Sep. 2022
- 村井紘子, MIMS/CMMA トポロジーとその応用融合研究セミナー, Some mathematical treatments of flat foldable and/or rigid foldable origami, Public discourse, 15 Feb. 2024, 15 Feb. 2024, 15 Feb. 2024
- 村井紘子, 文科省共同利用・共同研究拠点 MIMS「現象数理学研究拠点」共同研究集会「折り紙の科学を基盤とするアート・数理および工学への応用Ⅳ」, トポロジーと折り紙ー folding motion を許容しない folded state の存在についてー, Invited oral presentation, 16 Dec. 2023, 15 Dec. 2023, 16 Dec. 2023
- Hiroko Murai; Akari Iwamura, 10th International Congress on Industrial and Applied Mathematics, A remark on the foldability of non-simply connected paper, Oral presentation, 23 Aug. 2023, 20 Aug. 2023, 25 Aug. 2023
Research Projects
- Grant-in-Aid for Young Scientists (B), 2009, 2012, 21740055, Foliations on three dimensional manifolds, MURAI Hiroko, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Nara Women's University, 0, 0, 0, We studied intersections of essential laminations and Heegaard surfaces which give strongly irreducible Heegaard splittings in three dimensional manifolds. It is known that such Heegaard surfaces intersect essential surfaces in essential simple closed curves. We gave a similar result when Heegaard genus is two. We also gave some examples which give a phenomenon specific to non-compact objects., Competitive research funding, kaken
- 基盤研究(C), 01 Apr. 2022, 31 Mar. 2026, 22K03313, 大域構造の空間を基軸とする低次元トポロジーの研究とその応用, 小林 毅; 村井 紘子; 張 娟姫, 日本学術振興会, 科学研究費助成事業, 奈良女子大学, 3250000, 2500000, 750000, kaken;rm:presentations;rm:presentations;rm:presentations
- 基盤研究(C), 01 Apr. 2023, 31 Mar. 2027, 23K03231, 位相幾何学による折り紙理論の新しい展開とその応用, 村井 紘子, 日本学術振興会, 科学研究費助成事業, 奈良女子大学, 2600000, 2000000, 600000, kaken;rm:presentations;rm:presentations;rm:presentations
- Grant-in-Aid for Scientific Research (C), 01 Apr. 2013, 31 Mar. 2017, 25400091, Research on 3-manifold using geometric techniques and its development, Kobayashi Tsuyoshi; BAKER Kenneth; FUNAKOSHI Yukari; HASHIZUME Megumi; IDO Ayako; ICHIHARA Kazuhiro; ITO Noboru; JANG Yeonhee; MURAI Hiroko; OZAWA Makoto; TAKAO Kazuto; RIECK Yo'av, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Nara Women's University, 3900000, 3000000, 900000, In this research, we show that, for each n >1, there exist a Heegaard splitting with distance n, and there exists a bridge splitting with distance n. We introduce a new concept on Heegaard theory, called keen Heegaard splitting, and develop the techniques to show that there are keen Heegaard splittings with distance n. Then we show that there are knots each of which admits infinitely many irreducible bridge spheres with arbitrarily high bridge index. We apply the idea of similarity structure on 2-dimensional torus to construct flat foldable origami. Further we show that there are flat foldable origamis that are not constructed by using similarity structure. In addition to these, we define a distance on the set of isotopy classes of the spherical curves, and give some results on it., kaken