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Motoko Kotani

Section

Board Member

Job title

Executive Vice President

Degree

理学博士（東京都立大学）
理学修士（東京都立大学）

researchmap

https://researchmap.jp/motoko0101

J-GLOBAL ID

201101053089477541

Profile

現：東北大学理事（非常勤）（研究国際戦略・展開）

日本学術会議会員（２３、２４期）
日本数学会理事(2015-2016 理事長）

専門分野：数学，特に離散幾何解析学

科研費新学術領域次世代物質探索のための離散幾何
https://www.math-materials.jp/
CREST 熱可塑性エラストマーにおける動的ネットワークのトポロジー制御（中嶋健代表）
で数学と物質科学の出会い、広がりを追求しています。

履歴：
１９８３年東京大学理学部数学科卒業
１９９０年理学博士
１９９９年東北大学大学院理学研究科助教授を経て現職
２０１２年東北大学材料科学高等研究所長（WPI-AIMR)

２００５年第２５回猿橋賞受賞

海外研究歴
1993年9月〜1994年 8月：ドイツ，マックスプランク研究所
2001年4月〜11月：フランス，高等科学研究所(IHES)
2006年2月〜3月：イギリス，ニュートン研究所

Research History 6

2017/04 - Present

Tohoku University　Advanced Institute for Materials Research (AIMR)　Principal Investigator, Professor
2004 - Present

Tohoku University　Graduate School of Science　Professor
2011/03 - 2017/03

Tohoku University　Advanced Institute for Materials Research (AIMR)　Principal Investigator, Professor
1999 - 2003

Tohoku University　Graduate School of Science　Associate Professor
1997 - 1999

Toho University　Faculty of Science　Associate Professor
1990 - 1997

Toho University　Faculty of Science　Lecturer

Show all Show first 5

Professional Memberships 2

日本応用数理学会
日本数学会

Research Interests 11

geometric analysis
discrete geometry
グラフ
離散幾何解析
距離空間
グロモフ・ハウスドルフ収束
スペクトル
離散群
ランダムウォーク
調和写像
結晶格子

Research Areas 3

Natural sciences / Geometry / discrete geometry, geometric analsis
Natural sciences / Mathematical analysis /
Natural sciences / Geometry /

Awards 1

Saruhashi Prize

2005/05

Papers 82

Linear regression model for metal-organic frameworks with CO2 adsorption based on topological data analysis. International-journal

Kazuto Akagi, Hisashi Naito, Takafumi Saikawa, Motoko Kotani, Hirofumi Yoshikawa

Scientific reports　14　(1)　12021-12021　2024/05/26

DOI： 10.1038/s41598-024-62858-7 　

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Metal-organic frameworks (MOFs), self-assembled porous materials synthesized from metal ions and organic ligands, are promising candidates for the direct capture of CO2 from the atmosphere. In this work, we developed a regression model to predict the optimal component of the MOF that governs the amount of CO2 adsorption per volume based on experimentally observed adsorption and structure data combined with MOF adsorption sites. The structural descriptors were generated by topological data analysis with persistence diagrams, an advanced mathematical method for quantifying the rings and cavities within the MOF. This enables us to analyze direct effects and significance of the geometric structure of the MOF on the efficiency of CO2 adsorption in a novel way. The proposed approach is proved to be highly correlated with experimental data and thus offers an effective screening tool for MOFs with optimized structures.
A Weierstrass Representation Formula for Discrete Harmonic Surfaces

Motoko Kotani, Hisashi Naito

SIGMA　20 (2024)　(034)　15 pages　2024/04

DOI： 10.3842/SIGMA.2024.034 　

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Abstract A discrete harmonic surface is a trivalent graph which satisfies the balancing condition in the 3-dimensional Euclidean space and achieves energy minimizing under local deformations. Given a topological trivalent graph, a holomorphic function, and an associated discrete holomorphic quadratic form, a version of the Weierstrass representation formula for discrete harmonic surfaces in the 3-dimensional Euclidean space is proposed. By using the formula, a smooth converging sequence of discrete harmonic surfaces is constructed, and its limit is a classical minimal surface defined with the same holomorphic data. As an application, we have a discrete approximation of the Enneper surface.
A mathematical model of thermoplastic elastomers for analysing the topology of microstructures and mechanical properties during elongation Peer-reviewed

Hiroki Kodama†, Hiroshi Morita, Motoko Kotani

Proc. R. Soc. A　480　(2286)　2024/03

DOI： 10.1098/rspa.2023.0389 　

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Abstract In this study, a mathematical model based on graph theory is developed to analyse the deformed structures and mechanical properties of thermoplastic elastomers (TPEs) using ABA-type triblock copolymers. TPEs exhibit a network structure formed by bridge chains; deformation of this network structure causes stress. During the deformation of TPEs, domain breakage and coalescence occur, accompanied by topological changes in the chains, such as conformational transitions between the bridge and loop chains. By employing the mathematical concepts of harmonic realization of graphs in the physical space and the tension tensor to quantify the stress in the bridge-chain network structure, an effective method for analysing topologicalchanges in microstructures caused by elongation is proposed. As an application of this method, optimal geometric structures of block copolymers with desired functionalities can be determined.
Prominent Structural Dependence of Quantum Capacitance Unraveled by Nitrogen‐Doped Graphene Mesosponge

Rui Tang, Alex Aziz, Wei Yu, Zheng‐Ze Pan, Ginga Nishikawa, Takeharu Yoshii, Keita Nomura, Erin E. Taylor, Nicholas P. Stadie, Kazutoshi Inoue, Motoko Kotani, Takashi Kyotani, Hirotomo Nishihara

Small　2023/12/06
Publisher: Wiley
DOI： 10.1002/smll.202308066 　

ISSN： 1613-6810

eISSN： 1613-6829

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Abstract Porous carbons are important electrode materials for supercapacitors. One of the challenges associated with supercapacitors is improving their energy density without relying on pseudocapacitance, which is based on fast redox reactions that often shorten device lifetimes. A possible solution involves achieving high total capacitance (C_tot), which comprises Helmholtz capacitance (C_H) and possibly quantum capacitance (C_Q), in high‐surface carbon materials comprising minimally stacked graphene walls. In this work, a templating method is used to synthesize 3D mesoporous graphenes with largely identical pore structures (≈2100 m² g⁻¹ with an average pore size of ≈7 nm) but different concentrations of oxygen‐containing functional groups (0.3–6.7 wt.%) and nitrogen dopants (0.1–4.5 wt.%). Thus, the impact of the heteroatom functionalities on C_tot is systematically investigated in an organic electrolyte excluding the effect of pore structures. It is found that heteroatom functionalities determine C_tot, resulting in the cyclic voltammetry curves being rectangular or butterfly‐shaped. The nitrogen functionalities are found to significantly enhance C_tot owing to increased C_Q.
Edge-Site-Free and Topological-Defect-Rich Carbon Cathode for High-Performance Lithium-Oxygen Batteries. International-journal

Wei Yu, Takeharu Yoshii, Alex Aziz, Rui Tang, Zheng-Ze Pan, Kazutoshi Inoue, Motoko Kotani, Hideki Tanaka, Eva Scholtzová, Daniel Tunega, Yuta Nishina, Kiho Nishioka, Shuji Nakanishi, Yi Zhou, Osamu Terasaki, Hirotomo Nishihara

Advanced science (Weinheim, Baden-Wurttemberg, Germany)　10　(16)　e2300268　2023/04/07

DOI： 10.1002/advs.202300268 　

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The rational design of a stable and catalytic carbon cathode is crucial for the development of rechargeable lithium-oxygen (LiO2 ) batteries. An edge-site-free and topological-defect-rich graphene-based material is proposed as a pure carbon cathode that drastically improves LiO2 battery performance, even in the absence of extra catalysts and mediators. The proposed graphene-based material is synthesized using the advanced template technique coupled with high-temperature annealing at 1800 °C. The material possesses an edge-site-free framework and mesoporosity, which is crucial to achieve excellent electrochemical stability and an ultra-large capacity (>6700 mAh g-1 ). Moreover, both experimental and theoretical structural characterization demonstrates the presence of a significant number of topological defects, which are non-hexagonal carbon rings in the graphene framework. In situ isotopic electrochemical mass spectrometry and theoretical calculations reveal the unique catalysis of topological defects in the formation of amorphous Li2 O2 , which may be decomposed at low potential (∼ 3.6 V versus Li/Li+ ) and leads to improved cycle performance. Furthermore, a flexible electrode sheet that excludes organic binders exhibits an extremely long lifetime of up to 307 cycles (>1535 h), in the absence of solid or soluble catalysts. These findings may be used to design robust carbon cathodes for LiO2 batteries.
Mathematical Description for the Hierarchy of Grain-boundary Structures

Kazutoshi INOUE, Motoko KOTANI, Yuichi IKUHARA

Vacuum and Surface Science　66　(3)　146-151　2023/03/10
Publisher: Surface Science Society Japan
DOI： 10.1380/vss.66.146 　

ISSN： 2433-5835 2433-5843

eISSN： 2433-5843

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Polycrystalline materials are ubiquitous, and their macroscopic properties strongly depend on the defects in crystalline structures. Grain boundaries (GBs) are the interfaces between crystal grains, which admit unique atomic arrangements different from those of crystals. It is essential to reveal the polyhedral arrangement in GB atomic structures to identify the origin of structure-property relationships in polycrystalline materials. We found that the GB region can only be packed by the bulk or GB-type polyhedral units with minor variations. Moreover, the GB hierarchy directly follows the distribution of rational numbers that is represented by the Farey diagram. The singular GB is defined to be a GB packed by at the most two types of polyhedral units in a period, and any GB can be packed by the polyhedral units that form the singular GBs. This approach allows us to predict the polyhedral arrangement in any tilt GBs including random GBs.
Capacitance of edge-free three-dimensional graphene: New perspectives on the design of carbon structures for supercapacitor applications

Rui Tang, Keita Nomura, Kazutoshi Inoue, Motoko Kotani, Takashi Kyotani, Hirotomo Nishihara

Electrochimica Acta　429　2022/10/10

DOI： 10.1016/j.electacta.2022.141009 　

ISSN： 0013-4686
Coexistence of Urbach‐Tail‐Like Localized States and Metallic Conduction Channels in Nitrogen‐Doped 3D Curved Graphene Peer-reviewed

Yoichi Tanabe, Yoshikazu Ito, Katsuaki Sugawara, Samuel Jeong, Tatsuhiko Ohto, Tomohiko Nishiuchi, Naoaki Kawada, Shojiro Kimura, Christopher Florencio Aleman, Takashi Takahashi, Motoko Kotani, Mingwei Chen

Advanced Materials　34　2205986　2022/10

DOI： 10.1002/adma.202205986 　

ISSN： 0935-9648

eISSN： 1521-4095
Construction of continuum from a discrete surface by its iterated subdivisions

Motoko Kotani, Hisashi Naito, Chen Tao

Tohoku Mathematical Journal　74　(2)　2022/06/01
Publisher: Mathematical Institute, Tohoku University
DOI： 10.2748/tmj.20201225 　

ISSN： 0040-8735
Arrangement of polyhedral units for [0001]-symmetrical tilt grain boundaries in zinc oxide

Kazutoshi Inoue, Ji-Young Roh, Kazuaki Kawahara, Mitsuhiro Saito, Motoko Kotani, Yuichi Ikuhara

Acta Materialia　212　116864-116864　2021/06
Publisher: Elsevier BV
DOI： 10.1016/j.actamat.2021.116864 　

ISSN： 1359-6454
Geometric model of 3D curved graphene with chemical dopants Peer-reviewed

Andreas Dechant, Tatsuhiko Ohto, Yoshikazu Ito, Marina V. Makarova, Yusuke Kawabe, Tatsufumi Agari, Hikaru Kumai, Yasufumi Takahashi, Hisashi Naito, Motoko Kotani

Carbon　182　223-232　2021/06

DOI： 10.1016/j.carbon.2021.06.004 　

ISSN： 0008-6223

eISSN： 1873-3891
3D arrangement of atomic polyhedra in tilt grain boundaries Peer-reviewed

Kazutoshi Inoue, Kazuaki Kawahara, Mitsuhiro Saito, Motoko Kotani, Yuichi Ikuhara

Acta Materialia　202　266-276　2020/10
Publisher: Elsevier BV
DOI： 10.1016/j.actamat.2020.10.017 　

ISSN： 1359-6454
A nitrogen-doped nanotube molecule with atom vacancy defects Peer-reviewed

Koki Ikemoto, Seungmin Yang, Hisashi Naito, Motoko Kotani, Sota Sato, Hiroyuki Isobe

Nature Communications　11　(1)　2020/03
Publisher: Springer Science and Business Media LLC
DOI： 10.1038/s41467-020-15662-6 　

eISSN： 2041-1723

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<title>Abstract</title>Nitrogen-doped carbon nanotubes have attracted attention in various fields, but lack of congeners with discrete molecular structures has hampered developments based on in-depth, chemical understandings. In this study, a nanotube molecule doped periodically with multiple nitrogen atoms has been synthesized by combining eight 2,4,6-trisubstituted pyridine units with thirty-two 1,3,5-trisubstituted benzene units. A synthetic strategy involving geodesic phenine frameworks is sufficiently versatile to tolerate pyridine units without requiring synthetic detours. Crystallographic analyses adopting aspherical multipole atom models reveal the presence of axially rotated structures as a minor disordered structure, which also provides detailed molecular and electronic structures. The nitrogen atoms on the nanotube serve as chemically distinct sites covered with negatively charged surfaces, and they increase the chance of electron injections by lowering the energy levels of the unoccupied orbitals that should serve as electron acceptors.
Recoverably and destructively deformed domain structures in elongation process of thermoplastic elastomer analyzed by graph theory Peer-reviewed

H. Morita, A. Miyamoto, M. Kotani

Polymer　188　122098　2020
Phase Separation Dynamics of a Binary Fluid with a Closed-Loop Phase Diagram Peer-reviewed

Masatoshi Toda, Shinji Kajimoto, Shuichi Toyouchi, Toshihiro Kawakatsu, Yohji Akama, Motoko Kotani, Hiroshi Fukumura

Journal of the Physical Society of Japan　88　(024007)　1-6　2019

DOI： 10.7566/JPSJ.88.024007 　
Time-Resolved Structured Illumination Microscopy for Phase Separation Dynamics of Water and 2-Butoxyethanol Mixtures: Interpretation of “Early Stage” Involving Micelle-Like Structures Peer-reviewed

Shuichi Toyouchi, Shinji Kajimoto, Masatoshi Toda, Toshihiro Kawakatsu, Yohji Akama, Motoko Kotani, Hiroshi Fukumura J

The Journal of Physical Chemistry B　1-50　2018/12

DOI： 10.1021/acs.jpcb.8b10244 　
Structure of Tilt Grain Boundaries from Mathematical Perspective Peer-reviewed

Kazutoshi Inoue, Motoko Kotani, Yuichi Ikuhara

九州大学マス・フォア・インダストリ研究所レクチャーノート　2017/12
A discrete surface theory Peer-reviewed

M. Kotani, H. Naito, T. Omori

Computer Aided Geometric Design　58　24-54　2017/11
Publisher: Elsevier BV
DOI： 10.1016/j.cagd.2017.09.002 　

ISSN： 0167-8396
- Peer-reviewed

KOTANI Motoko

Journal of the Japan Society of Polymer Processing　29　(11)　405-409　2017/11
Publisher:
DOI： 10.2320/materia.56.589 　

ISSN： 0915-4027
Analysis of Periodic Atomic Structures in Grain Boundaries by Number Theory Peer-reviewed

Inoue Kazutoshi, Saito Mitsuhiro, Kotani Motoko, Ikuhara Yuichi

Materia Japan　56　(10)　589-596　2017/10
Publisher: The Japan Institute of Metals and Materials
DOI： 10.2320/materia.56.589 　

ISSN： 1340-2625
Structure of <110> -tilt boundaries in cubic zirconia Peer-reviewed

Kazutoshi Inoue, Bin Feng, Naoya Shibata, Motoko Kotani, Yuichi Ikuhara

JOURNAL OF MATERIALS SCIENCE　52　(8)　4278-4287　2017/04

DOI： 10.1007/s10853-016-0682-1 　

ISSN： 0022-2461

eISSN： 1573-4803
Asymptotic expansion of the transition probability for non-symmetric random walks on crystal lattices Peer-reviewed

Ishiwata Satoshi, Kawabi Hiroshi, Kotani Motoko

数理解析研究所講究録　2023　(2023)　15-28　2017/04
Publisher:
ISSN： 1880-2818
Long time asymptotes of non-symmetric random walks on crystal lattices Peer-reviewed

Satoshi Ishiwata, Hiroshi Kawabi, Motoko Kotani

JOURNAL OF FUNCTIONAL ANALYSIS　272　(4)　1553-1624　2017/02

DOI： 10.1016/j.jfa.2016.11.011 　

ISSN： 0022-1236

eISSN： 1096-0783
Mathematical analysis and STEM observations of arrangement of structural units in <001> symmetrical tilt grain boundaries Peer-reviewed

Kazutoshi Inoue, Mitsuhiro Saito, Chunlin Chen, Motoko Kotani, Yuichi Ikuhara

MICROSCOPY　65　(6)　479-487　2016/12

DOI： 10.1093/jmicro/dfw034 　

ISSN： 2050-5698

eISSN： 2050-5701
Phase behavior of a binary fluid mixture of quadrupolar molecules Peer-reviewed

Masatoshi Toda, Shinji Kajimoto, Shuichi Toyouchi, Toshihiro Kawakatsu, Yohji Akama, Motoko Kotani, Hiroshi Fukumura

PHYSICAL REVIEW E　94　(5)　052601-052601　2016/11

DOI： 10.1103/PhysRevE.94.052601 　

ISSN： 2470-0045

eISSN： 2470-0053
Stereoisomerism in Nanohoops with Heterogeneous Biaryl Linkages of E/Z- and R/S-Geometries Peer-reviewed

Parantap Sarkar, Zhe Sun, Toshiki Tokuhira, Motoko Kotani, Sota Sato, Hiroyuki Isobe

ACS CENTRAL SCIENCE　2　(10)　740-747　2016/10

DOI： 10.1021/acscentsci.6b00240 　

ISSN： 2374-7943

eISSN： 2374-7951
Stereoisomerism, crystal structures, and dynamics of belt-shaped cyclonaphthylenes Peer-reviewed

Zhe Sun, Takuya Suenaga, Parantap Sarkar, Sota Sato, Motoko Kotani, Hiroyuki Isobe

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA　113　(29)　8109-8114　2016/07

DOI： 10.1073/pnas.1606530113 　

ISSN： 0027-8424
- Peer-reviewed

Kazutoshi Inoue, Chunlin Chen, Motoko Kotani, Yuichi Ikuhara

まてりあ　55　(12)　582-582　2016
Publisher: The Japan Institute of Metals and Materials
DOI： 10.2320/materia.55.582 　
Materials inspired by mathematics Peer-reviewed

Motoko Kotani, Susumu Ikeda

SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS　17　(1)　253-259　2016

DOI： 10.1080/14686996.2016.1180233 　

ISSN： 1468-6996

eISSN： 1878-5514
Breakthroughs Based on the Mathematics-Materials Science Collaboration Peer-reviewed

Susumu Ikeda, Motoko Kotani

A New Direction in Mathematics for Materials Science　69-75　2015/12
Influence of Mathematics on Materials Science Upto Date Peer-reviewed

Susumu Ikeda, Motoko Kotani

A New Direction in Mathematics for Materials Science　11-50　2015/12
Some Specific Examples of Mathematics-Materials Science Collaboration at AIMR Peer-reviewed

Susumu Ikeda, Motoko Kotani

A New Direction in Mathematics for Materials Science　51-67　2015/12
A Historical View of Materials Science Peer-reviewed

Susumu Ikeda, Motoko Kotani

A New Direction in Mathematics for Materials Science　1-9　2015/12
The Decomposition Formula of < 001 > Symmetrical Tilt Grain Boundaries Peer-reviewed

Kazutoshi Inoue, Mitsuhiro Saito, Zhongchang Wang, Motoko Kotani, Yuichi Ikuhara

MATERIALS TRANSACTIONS　56　(12)　1945-1952　2015/12

DOI： 10.2320/matertrans.M2015277 　

ISSN： 1345-9678

eISSN： 1347-5320
- Peer-reviewed

Ishiwata Satoshi, Kawabi Hiroshi, Kotani Motoko

-　1952　(1952)　30-37　2015/06
Publisher:
ISSN： 1880-2818
Visualization of topological landscape in shear-flow dynamics of amorphous solids Peer-reviewed

Takeshi Fujita, Koji Ohara, Keiji Miura, Akihiko Hirata, Motoko Kotani, Yasumasa Nishiura, Mingwei Chen

EPL　110　(3)　38002-38002　2015/05

DOI： 10.1209/0295-5075/110/38002 　

ISSN： 0295-5075

eISSN： 1286-4854
24pAQ-3 Phase separation dynamics of a binary mixture with a closed-loop phase diagram Peer-reviewed

M. Toda, S. Kajimoto, S. Toyouchi, T. Kawakatsu, Y. Akama, M. Kotani, H. Fukumura

Meeting Abstracts of the Physical Society of Japan　70.1　(0)　3438-3438　2015
Publisher: The Physical Society of Japan (JPS)
DOI： 10.11316/jpsgaiyo.70.1.0_3438 　

ISSN： 2189-079X
A new direction in mathematics for materials science Peer-reviewed

Ikeda, Susumu, Kotani, Motoko

Springer Briefs in the Mathematics of Materials　1　1-86　2015
22aCJ-6 Mathematical Approach to Problems in Solid State Physics Peer-reviewed

KOTANI Motoko

Meeting Abstracts of the Physical Society of Japan　70.1　(0)　2727-2727　2015
Publisher: The Physical Society of Japan (JPS)
DOI： 10.11316/jpsgaiyo.70.1.0_2727 　

ISSN： 2189-079X
On the Periodicity of < 001 > Symmetrical Tilt Grain Boundaries Peer-reviewed

Kazutoshi Inoue, Mitsuhiro Saito, Zhongchang Wang, Motoko Kotani, Yuichi Ikuhara

MATERIALS TRANSACTIONS　56　(3)　281-287　2015

DOI： 10.2320/matertrans.M2014394 　

ISSN： 1345-9678

eISSN： 1347-5320
Mesoscopic Dynamics of Laser-induced Phase Separation in Water and 2-Butoxyethanol Mixtures Revealed by Nanosecond Time-resolved Light Scattering Peer-reviewed

Shuichi Toyouchi, Shinji Kajimoto, Masatoshi Toda, Toshihiro Kawakatsu, Yohji Akama, Motoko Kotani, Hiroshi Fukumura

CHEMISTRY LETTERS　43　(12)　1838-1840　2014/12

DOI： 10.1246/cl.140698 　

ISSN： 0366-7022

eISSN： 1348-0715
Quantization of interface currents Peer-reviewed

Motoko Kotani, Hermann Schulz-Baldes, Carlos Villegas-Blas

JOURNAL OF MATHEMATICAL PHYSICS　55　(12)　2014/12

DOI： 10.1063/1.4902377 　

ISSN： 0022-2488

eISSN： 1089-7658
Negatively curved cubic carbon crystals with octahedral symmetry Peer-reviewed

Makoto Tagami, Yunye Liang, Hisashi Naito, Yoshiyuki Kawazoe, Motoko Kotani

CARBON　76　266-274　2014/09

DOI： 10.1016/j.carbon.2014.04.077 　

ISSN： 0008-6223

eISSN： 1873-3891
Geometric measures of finite carbon nanotube molecules: a proposal for length index and filling indexes Peer-reviewed

Taisuke Matsuno, Hisashi Naito, Shunpei Hitosugi, Sota Sato, Motoko Kotani, Hiroyuki Isobe

PURE AND APPLIED CHEMISTRY　86　(4)　489-495　2014/04

DOI： 10.1515/pac-2014-5006 　

ISSN： 0033-4545

eISSN： 1365-3075
New phase of materials science based on discrete geometric analysis:——Achievements of AMF/CREST/SMART/WPI-AIMR—— Peer-reviewed

Kotani Motoko

SUGAKU　65　(3)　299-303　2013/07/25
Publisher: The Mathematical Society of Japan
DOI： 10.11429/sugaku.0653299-2 　

ISSN： 0039-470X
Geometric Frustration of Icosahedron in Metallic Glasses Peer-reviewed

A. Hirata, L. J. Kang, T. Fujita, B. Klumov, K. Matsue, M. Kotani, A. R. Yavari, M. W. Chen

SCIENCE　341　(6144)　376-379　2013/07

DOI： 10.1126/science.1232450 　

ISSN： 0036-8075
A Mathematical Challenge to a New Phase of Materials Science Peer-reviewed

Motoko Kotani

Bulletin of the Japan Society for Industrial and Applied Mathematics　23　(4)　150-153　2013
Publisher: The Japan Society for Industrial and Applied Mathematics
DOI： 10.11540/bjsiam.23.4_150 　

ISSN： 0917-2270

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Demands for new mathematical theories to describe nano-scale phenomena are increasing. The project to meet them and to develop mathematical models has been supported by JST CREST from 2008 to 2013. Under the projects, we set four research subjects: 1. Design of K4 Lattice (Sunada Lattice) Characteristics and Its Synthesis, 2. Development of Structured Illumination, 3. Analysis of Ultrafast Phase Separation Dynamics, 4. Achievement of High Heat-Conductivity in Heat-Resistant Polymers. In the present article and the following articles, some of our mathematical challenges are discussed.
数学・数理科学の新たな潮流：諸科学との連携を求めて Peer-reviewed

Motoko Kotani

Hyomen Kagaku　34　(1)　2-2　2013

DOI： 10.1380/jsssj.34.2 　

ISSN： 0388-5321
A Challenge by Mathematics-Materials Science Collaboration Peer-reviewed

Motoko Kotani

Hyomen Kagaku　34　(1)　3-8　2013
Publisher:
DOI： 10.1380/jsssj.34.3 　

ISSN： 0388-5321
Effect of molecular geometry on LCST-type phase separation Peer-reviewed

M. Toda, S. Kajimoto, T. Kawakatsu, Y. Akama, M. Kotani, H. Fukumura

Meeting Abstracts of the Physical Society of Japan　68.2.2　321-321　2013

DOI： 10.11316/jpsgaiyo.68.2.2.0_321_3 　
New Growth Mechanism of Cubic Rh Clusters Composed of 8-12 Atoms Found by the Method of Euclidean Designs Peer-reviewed

Makoto Tagami, Yunye Liang, Yoshiyuki Kawazoe, Motoko Kotani

MATERIALS TRANSACTIONS　53　(3)　459-462　2012/03

DOI： 10.2320/matertrans.N-M2011859 　

ISSN： 1345-9678

eISSN： 1347-5320
Probabilistic Approach to Geometry Peer-reviewed

Motoko Kotani, M. Hino, T. Kumagai

Advanced Studies in Pure Mathematics　57　1-540　2010/03
Publisher:
DOI： 10.1142/e025 　
New Metallic Carbon Crystal Peer-reviewed

Masahiro Itoh, Motoko Kotani, Hisashi Naito, Toshikazu Sunada, Yoshiyuki Kawazoe, Tadafumi Adschiri

PHYSICAL REVIEW LETTERS　102　(5)　055703　2009/02

DOI： 10.1103/PhysRevLett.102.055703 　

ISSN： 0031-9007

eISSN： 1079-7114
Spectral Analysis in Geometry and Number Theory - Contemporary Mathematics Peer-reviewed

M. Kotani, H. Naito, T. Tate

484　1-342　2009
Discrete Analysis of Crystal Lattices Invited Peer-reviewed

Motoko Kotani

Sugaku Expositions　19　(2)　117-134　2006/12
Large deviation and the tangent cone at infinity of a crystal lattice Peer-reviewed

Motoko Kotani, Toshikazu Sunada

MATHEMATISCHE ZEITSCHRIFT　254　(4)　837-870　2006/12

DOI： 10.1007/s000209-006-0951-9 　

ISSN： 0025-5874
Noncommutativity and Singularities, Proceedings of French--apanese symposia Held at IH?S in 2007 Peer-reviewed

J.-P. Bourguignon, M. Kotani, Y. Maeda, N. Tose

55　1-363　2006/07

DOI： 10.1142/e020 　
Symmetry in the Discrete Geometric Analysis(Invited Lectures in the 15th JSIAM Annual Meeting) Invited Peer-reviewed

Kotani Motoko

Bulletin of the Japan Society for Industrial and Applied Mathematics　16　(1)　69-73　2006
Publisher: The Japan Society for Industrial and Applied Mathematics
DOI： 10.11540/bjsiam.16.1_69 　

ISSN： 0917-2270
Discrete Geometric Analysis: Proceedings of the First JAMS Symposium on Discrete Geometric Analysis, December 12-20, 2003, Sendai, Japan Peer-reviewed

M. Kotani, T. Shirai, T. Sunada

Contemporary Mathematics　347　1-258　2004/04
An asymptotic of the large deviation for random walks on a crystal lattice Peer-reviewed

Motoko Kotani

contemporary mathematics　347　141-152　2004
Lipschitz continuity of the spectra of the magnetic transition operators on a crystal lattice Peer-reviewed

Motoko Kotani

Journal of Geometry and Physics　47　(2-3)　323-342　2003/08

DOI： 10.1016/S0393-0440(02)00226-7 　

ISSN： 0393-0440
Spectral Geometry of Crystal lattices Invited Peer-reviewed

Motoko Koani, Toshikazu Sunada

contemp. math.　338　271-305　2003
Discrete geometrical analysis from the viewpoint of crystal lattices Peer-reviewed

Motoko Kotani

Sugaku　54　(4)　348-364　2002/10/25
Publisher:
DOI： 10.11429/sugaku1947.54.348 　

ISSN： 0039-470X
A central limit theorem for magnetic transition operators on a crystal lattice Peer-reviewed

Motoko Kotani

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES　65　464-482　2002/04

DOI： 10.1112/S0024610701002770 　

ISSN： 0024-6107
Geometrical aspect of large deviation for random walks on a crystal lattice Invited Peer-reviewed

Motoko Kotani, Toshikazu Sunada

Microlocal analysis and complex Fourier analysis　215-223　2002
GEOMETRIC ASPECTS OF LARGE DEVIATIONS FOR RANDOM WALKS ON A CRYSTAL LATTICE (Geometry of Submanifolds and Related Topics)

Kotani Motoko, Sunada Toshikazu

RIMS Kokyuroku　1236　(1236)　112-114　2001/11
Publisher: Kyoto University
ISSN： 1880-2818
A note on asymptotic expansions for closed geodesics in homology classes Peer-reviewed

M Kotani

MATHEMATISCHE ANNALEN　320　(3)　507-529　2001/07

DOI： 10.1007/s002080100210 　

ISSN： 0025-5831
The pressure and higher correlations for an Anosov diffeomorphism Peer-reviewed

M Kotani, T Sunada

ERGODIC THEORY AND DYNAMICAL SYSTEMS　21　807-821　2001/06

DOI： 10.1017/S0143385701001407 　

ISSN： 0143-3857
Jacobian tori associated with a finite graph and its Abelian covering graphs Peer-reviewed

M Kotani, T Sunada

ADVANCES IN APPLIED MATHEMATICS　24　(2)　89-110　2000/02

DOI： 10.1006/aama.1999.0672 　

ISSN： 0196-8858
Albanese Maps and Off Diagonal Long Time Asymptotics for the Heat Kernel

Motoko Kotani, Toshikazu Sunada

Communications in Mathematical Physics　209　(3)　633-670　2000/02/01
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s002200050033 　

ISSN： 0010-3616

eISSN： 1432-0916
Standard realizations of crystal lattices via harmonic maps Peer-reviewed

M Kotani, T Sunada

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY　353　(1)　1-20　2000

ISSN： 0002-9947
Zeta functions of finite graphs Peer-reviewed

KOTANI Motoko

Journal of Mathematcal Science, University of Tokyo　7　(1)　7-25　2000
Publisher: The University of Tokyo
ISSN： 1340-5705
A central limit theorem for the simple random walk on a crystal lattice Peer-reviewed

M Kotani, T Sunada

PROCEEDINGS OF THE SECOND ISAAC CONGRESS, VOLS 1 AND 2　7　1-6　2000
Asymptotic behavior of the transition probability of a random walk on an infinite graph Peer-reviewed

M Kotani, T Shirai, T Sunada

JOURNAL OF FUNCTIONAL ANALYSIS　159　(2)　664-689　1998/11

DOI： 10.1006/jfan.1998.3322 　

ISSN： 0022-1236
Harmonic 2-spheres with r pairs of extra eigenfunctions Peer-reviewed

M Kotani

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY　125　(7)　2083-2092　1997/07

ISSN： 0002-9939
ON THE FUNDAMENTAL GROUP OF THE SPACE OF HARMONIC 2-SPHERES IN THE N-SPHERE Peer-reviewed

M FURUTA, MA GUEST, M KOTANI, Y OHNITA

MATHEMATISCHE ZEITSCHRIFT　215　(4)　503-518　1994/04

ISSN： 0025-5874
CONNECTEDNESS OF THE SPACE OF MINIMAL 2-SPHERES IN S(2M)(1) Peer-reviewed

M KOTANI

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY　120　(3)　803-810　1994/03

ISSN： 0002-9939
Index and flat ends of minimal surface Peer-reviewed

KOTANI Motoko

Tokyo Journal of Mathematics　16　37-46　1993
MINIMAL-SURFACES IN S(2M)(1) WITH EXTRA EIGENFUNCTIONS Peer-reviewed

N EJIRI, M KOTANI

QUARTERLY JOURNAL OF MATHEMATICS　43　(172)　421-440　1992/12

ISSN： 0033-5606
A DECOMPOSITION THEOREM OF 2-TYPE IMMERSIONS Peer-reviewed

M KOTANI

NAGOYA MATHEMATICAL JOURNAL　118　55-64　1990/06

DOI： 10.1017/S0027763000002993 　

ISSN： 0027-7630
An immersion of an n-dimensional real space form into an n-dimensional complex space form Peer-reviewed

Motoko Kotani

Tokyo Journal of Mathematics　9　(1)　103-113　1986

DOI： 10.3836/tjm/1270150980 　

ISSN： 0387-3870
THE 1ST EIGENVALUE OF HOMOGENEOUS MINIMAL HYPERSURFACES IN A UNIT-SPHERE SN+1(1) Peer-reviewed

M KOTANI

TOHOKU MATHEMATICAL JOURNAL　37　(4)　523-532　1985/12

ISSN： 0040-8735

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Misc. 65

Mathematical Approaches in Materials Research

KOTANI Motoko

Vacuum and Surface Science　66　(3)　133-133　2023/03/10
Publisher: The Japan Society of Vacuum and Surface Science
DOI： 10.1380/vss.66.133 　

ISSN： 2433-5835

eISSN： 2433-5843
離散幾何解析とは

小谷元子

数理科学　61　(1)　71-78　2023/01
Publisher: サイエンス社
ISSN： 0386-2240
数理活用産学連携イニシアティブ : 数理科学と社会の相互作用を起こすためには—特集ポストコロナの社会における科学技術イノベーションの役割

小谷元子

経団連 / 日本経済団体連合会編　69　(9)　46-48　2021/09
Publisher: 日本経済団体連合会
ISSN： 2187-1485
African Institute for Mathematical Sciences (AIMS)―Finding the Next Einstein in Africa

Kimura Yoshifumi, Kotani Motoko

Butsuri　76　(4)　226-228　2021/04/05
Publisher: The Physical Society of Japan
DOI： 10.11316/butsuri.76.4_226 　

ISSN： 0029-0181

eISSN： 2423-8872
特別インタビュー東北大学理事・副学長/総合科学技術・イノベーション会議議員小谷元子氏インタビュー : 第6期科学技術・イノベーション基本計画への期待

小谷元子, 岡谷重雄, 横尾淑子, 林和弘

STI horizon = STIホライズン : イノベーションの新地平を拓く　7　(3)　3-6　2021
Publisher: 文部科学省科学技術学術政策研究所科学技術動向研究センター
ISSN： 2189-8693
Interaction Between Mathematics and Society in the Era of Digitalization

KOTANI Motoko

TRENDS IN THE SCIENCES　25　(9)　9_72-9_75　2020/09/01
Publisher: Japan Science Support Foundation
DOI： 10.5363/tits.25.9_72 　

ISSN： 1342-3363

eISSN： 1884-7080
大人のための最先端理科(第209回)数学数学発展の歴史が伝える理論を「美しい」と感じる力

小谷元子

週刊ダイヤモンド = Diamond weekly　107　(14)　66-67　2019/04/06
Publisher: ダイヤモンド社
大人のための最先端理科(第202回)数学知的生命体を魅了する「素数」の秘密解明への挑戦

小谷元子

週刊ダイヤモンド = Diamond weekly　107　(7)　70-71　2019/02/16
Publisher: ダイヤモンド社
大人のための最先端理科(第195回)数学代数と幾何の発想を融合したN×Nマスの魔方陣の作り方

小谷元子

週刊ダイヤモンド = Diamond weekly　106　(48)　74-75　2018/12/15
Publisher: ダイヤモンド社
砂田利一氏の平成30年度文部科学大臣表彰科学技術賞受賞に寄せて

小谷元子

数学通信　23　(3)　28-33　2018/11
Publisher: 日本数学会
ISSN： 1342-1387
大人のための最先端理科(第188回)数学波なのに塊のように振る舞う不思議な「ソリトン」の数学

小谷元子

週刊ダイヤモンド = Diamond weekly　106　(41)　84-85　2018/10/27
Publisher: ダイヤモンド社
大人のための最先端理科(第182回)数学祝!柏原正樹博士チャーン賞日本で生まれた代数解析学

小谷元子

週刊ダイヤモンド = Diamond weekly　106　(35)　82-83　2018/09/15
Publisher: ダイヤモンド社
大人のための最先端理科（第176回）【数学】驚くべき方程式が生み出す生き物の世界の多様と複雑

Motoko Kotani

Diamond Weekly　106　(29)　100-101　2018/07/28
大人のための最先端理科（第170回）【数学】ミクロとマクロの世界を繋ぐ臨界現象の統一理論の魅力

Motoko Kotani

Diamond Weekly　106　(26)　64-65　2018/06/16
大人のための最先端理科（第164回）【数学】検索スピードが飛躍的にアップ常識外れの量子力学の数学

Motoko Kotani

Diamond Weekly　106　(17)　122-123　2018/04/28
大人のための最先端理科（第159回）【数学】元の場所に戻れるかどうか活用広がるランダムウォーク

Motoko Kotani

Diamond Weekly　106　(12)　72-73　2018/03/24
大人のための最先端理科（第154回）【数学】ニュートンの微積分学に匹敵日本数学者が築いた確率解析

Motoko Kotani

Diamond Weekly　106　(7)　86-87　2018/02/17
科学のための幾何学入門（５）Lie群、対象空間

Motoko Kotani

Chemistry Today　563　57-61　2018/02
大人のための最先端理科（第149回）【数学】偶然に支配される現象を予測できる「確率論」の世界

Motoko Kotani

Diamond Weekly　106　(2)　74-75　2018/01/13
大人のための最先端理科（第144回）【数学】コンピュータを使えば正しい？数学の「真理」の高いハードル

Motoko Kotani

Diamond Weekly　105　(46)　84-85　2017/12/02
Publisher: ダイヤモンド社
科学のための幾何学入門（4）行列群、結晶群

Motoko Kotani

Chemistry Today　561　(561)　58-61　2017/12
Publisher: 東京化学同人
ISSN： 0386-961X
大人のための最先端理科（第139回）【数学】自然界の「形」が美しい理由シャボン玉が教える普遍法則

Motoko Kotani

Diamond Weekly　105　(41)　90-91　2017/10/28
Publisher: ダイヤモンド社
科学のための幾何学入門（3）行列

Motoko Kotani

Chemistry Today　559　(559)　64-67　2017/10
Publisher: 東京化学同人
ISSN： 0386-961X
大人のための最先端理科（第134回）【数学】データの法則を見出だす「曲率」素朴な発想で開かれた新次元

Motoko Kotani

Diamond Weekly　105　(36)　78-79　2017/09/23
Publisher: ダイヤモンド社
大人のための最先端理科（第129回）【数学】局所の情報から全体が見える最も美しいトポロジーの公式

Motoko Kotani

Diamond Weekly　105　(31)　84-85　2017/08/12
Publisher: ダイヤモンド社
科学のための幾何学入門（2）群の定義、群の積・商

Motoko Kotani

Chemistry Today　557　(557)　60-63　2017/08
Publisher: 東京化学同人
ISSN： 0386-961X
大人のための最先端理科（第124回）【数学】世紀の難問・ポアンカレ予想解明の裏に二つの幾何の交差

Motoko Kotani

Diamond Weekly　105　(26)　66-67　2017/07/08
Publisher: ダイヤモンド社
大人のための最先端理科（第119回）【数学】データを構造解明へつなげる数学と材料開発の意外な相性

Motoko Kotani

Diamond Weekly　105　(21)　80-81　2017/06/03
Publisher: ダイヤモンド社
離散と連続をつなぐ幾何（特集発展する微分幾何：その多様性、面白さ、そして美しさ）

小谷元子

数理科学　55　(6)　46-52　2017/06
Publisher: サイエンス社
ISSN： 0386-2240
科学のための幾何学入門（1）群と対称性（1）

Motoko Kotani

Chemistry Today　555　(555)　21-24　2017/06
Publisher: 東京化学同人
ISSN： 0386-961X
数学, 化学と出会う（６）柔らかさを数える

Motoko Kotani

Chemistry Today　545　(545)　22-24　2016/08
Publisher: 東京化学同人
ISSN： 0386-961X
数学, 化学と出会う（５）トポロジカル材料

Motoko Kotani

Chemistry Today　543　58-59　2016/06
数学, 化学と出会う（４）アモルファス材料のトポロジー解析

Motoko Kotani

Chemistry Today　541　60-61　2016/04
数学, 化学と出会う（３）柔らかい幾何学トポロジー

Motoko Kotani

Chemistry Today　539　(539)　15-17　2016/02
Publisher: 東京化学同人
ISSN： 0386-961X
2016 Spring Prize Winner Hiroshi Iritani

Kotani Motoko

SUGAKU　68　(4)　403-404　2016
Publisher: 一般社団法人日本数学会
ISSN： 0039-470X
数学, 化学と出会う（２）カーボンネットワークの対称性と曲がり方

Motoko Kotani

Chemistry Today　537　(537)　18-21　2015/12
Publisher: 東京化学同人
ISSN： 0386-961X
数学, 化学と出会う（１）怠け者の勧め

Motoko Kotani

Chemistry Today　535　(535)　19-22　2015/10
Publisher: 東京化学同人
ISSN： 0386-961X
結晶格子上の非対称ランダムウォークの中心極限定理 (Symposium on Probability Theory)

石渡聡, 河備浩司, 小谷元子

数理解析研究所講究録　1952　(1952)　30-37　2015/06
Publisher: 京都大学
ISSN： 1880-2818
待ち受ける心

小谷元子

数理科学臨時別冊数学的な感覚の探求　2014/11
Mackay-like all-carbon negatively curved crystals

LIANG Yunye, TAGAMI Makoto, NAITO Hisashi, KAWAZOE Yoshiyuki, KOTANI Motoko, HOSOKAWA Norikazu, OSHIMA Hisayoshi

ナノ学会大会講演予稿集　12th　162　2014/05/22

ISSN： 1347-8028
科学の泉材料科学への数学の挑戦?

小谷元子

河北新報　3面-3面　2013/08/04
科学の泉材料科学への数学の挑戦?

小谷元子

河北新報　3面-3面　2013/08/03
科学の泉材料科学への数学の挑戦?

小谷元子

河北新報　3面-3面　2013/08/02
科学の泉材料科学への数学の挑戦?

小谷元子

河北新報　3面-3面　2013/08/01
科学の泉材料科学への数学の挑戦?

小谷元子

河北新報　3面-3面　2013/07/31
科学の泉材料科学への数学の挑戦?

小谷元子

河北新報　3面-3面　2013/07/30
数学的な感覚の探求 : 思考法の源を探る(第10回)待ち受ける心

小谷元子

数理科学　51　(6)　63-67　2013/06
Publisher: サイエンス社
ISSN： 0386-2240
フロントランナー挑む第23回不連続なものの形の本質を探る

小谷元子

日経サイエンス　2013/01
Smart Innovation Based on Mathematics at Tohoku University(Laboratories)

Kotani Motoko

Bulletin of the Japan Society for Industrial and Applied Mathematics　22　(2)　151-153　2012
Publisher: The Japan Society for Industrial and Applied Mathematics
DOI： 10.11540/bjsiam.22.2_151 　

ISSN： 0917-2270
材料科学と離散幾何解析学の連携による挑戦

小谷元子

表面科学　34　(1)　3-8　2012

DOI： 10.1380/jsssj.34.3 　
東北大学数学連携の取り組み

小谷元子

応用数理　122　(2)　73-75　2012
数学・数理科学の新たな潮流―諸科学との連携を求めて

小谷元子

表面科学　34　(1)　2-2　2012
幾何と対称性：ダイヤモンドツイン？

小谷元子

日本評論社　47　(7)　23-28　2008/07
Publisher: 日本評論社
ISSN： 0386-4960
離散幾何への誘い（2）

小谷元子

数学セミナー　1　(1)　62-65　2006
Publisher: 日本評論社
ISSN： 0386-4960
解析学における０（特集０の発見ー無限なる可能性の開花）

小谷元子

数理科学　43　(11)　17-21　2005/11
Publisher: サイエンス社
ISSN： 0386-2240
〔日本数学会〕幾何分科会特別企画「21世紀の数学」出版の経緯

小谷元子

数学通信　9　(4)　28-30　2005/02
Publisher: 日本数学会
ISSN： 1342-1387
離散幾何への誘い（1）

小谷元子

数学セミナー　12　(12)　45-49　2005
Publisher: 日本評論社
ISSN： 0386-4960
グラフと作用素

小谷元子

数理科学　42　(4)　40-45　2004/04
Publisher: サイエンス社
ISSN： 0386-2240
グラフの幾何学--結晶格子の標準的実現と中心極限定理 (特集微分幾何の新世紀--応用数理,数理物理への展開)

小谷元子

数理科学　39　(2)　30-36　2001/02
Publisher: サイエンス社
ISSN： 0386-2240
グラフの幾何学

小谷元子

数理科学　39　(2)　30-36　2001/02/01
Publisher: サイエンス社
結晶格子を通してみる離散幾何解析

小谷元子

数学　54　(4)　2000/01
Publisher: 日本数学界
球面内の等質な極小超曲面の第一固有値について(リーマン多様体とリー群)

小谷元子

数理解析研究所講究録　576　48-64　1985/12
Publisher: 京都大学
ISSN： 1880-2818
RIMS International Workshop “Sapporo summer conference on dynamics of patterns in materials science”

Yasumasa Nishiura, Motoko Kotani

RIES, Hokkaido University (Sapporo) (Jul 31-Aug 02, 2014)
Mathematical approach to emerging topics in material science 2012

Yasumasa NISHIURA, Takayoshi OGAWA, Motoko KOTANI

WPI-AIMR, Tohoku University (Sendai) (Feb 18-19, 2012)
RIMS International Conference “Mathematical Challenge to a New Phase of Materials Science”

Yasumasa Nishiura, Motoko Kotani

Maskawa Hall, Kyoto University (Kyoto) (Aug 04-08, 2014)

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Books and Other Publications 29

離散幾何解析へのいざない : 数学から物質科学へ

小谷, 元子, 内藤, 久資

日本評論社　2025/06

ISBN: 9784535787223
離散幾何解析入門

小谷, 元子

岩波書店　2024/04

ISBN: 9784000299374
中学数学

坂井, 裕, 小谷, 元子

教育出版　2021/01

ISBN: 9784316204383
中学数学

坂井, 裕, 小谷, 元子

教育出版　2021/01

ISBN: 9784316204390
中学数学

坂井, 裕, 小谷, 元子

教育出版　2021/01

ISBN: 9784316204406
中学数学

坂井, 裕, 小谷, 元子

教育出版　2020

ISBN: 9784316204383
Operator algebras and mathematical physics

泉, 正己, 河東, 泰之, 小谷, 元子, 松井, 宏樹, 小沢, 登高

Mathematical Society of Japan　2019

ISBN: 9784864970792
Noncommutative geometry and physics 4

前田, 吉昭, 森吉, 仁志, 小谷, 元子, 綿村, 哲

World Scientific　2017

ISBN: 9789813144606
保険と金融の数理

室井芳史, 照井伸彦, 小谷元子, 赤間陽二, 花輪公雄

共立出版　2017

ISBN: 9784320111226
Mathematical challenges in a new phase of materials science : Kyoto, Japan, August 2014

Nishiura Yasumasa, 小谷元子

Springer　2016

ISBN: 9784431561026
現代日本と科学技術を巡る諸相

科学技術振興機構社会技術研究開発センター, 藤井威, 隈研吾, 野中郁次郎, 市川惇信, 中村桂子, 三浦公亮, 郷通子, 遠藤章, 小谷元子

丸善プラネット, 丸善出版 (発売)　2016

ISBN: 9784863452831
A new direction in mathematics for materials science

池田進, 小谷元子

Springer　2015

ISBN: 9784431558620
クロスセクショナル統計シリーズ

照井伸彦, 小谷元子, 赤間陽二, 花輪公雄

共立出版　2014
数学者が読んでいる本ってどんな本

小谷元子, 砂田利一, 黒川信重, 森重文, 上野健爾, 足立恒雄, 小谷元子, 益川敏英, 野崎昭弘, 高橋陽一郎, 深谷賢治, 高瀬正仁, 田中一之, 円城塔

東京図書　2013

ISBN: 9784489021640
Noncommutative geometry and physics 3 : Shonan Village Center, Japan, 18-22 February 2008 : Kyoto University, Japan, 1 April 2010-31 March 2011

Dito Giuseppe, 小谷元子, 前田吉昭, 森吉仁志, 夏目利一, 綿村哲

World Scientific　2013

ISBN: 9789814425001
宇宙の地図を描く : 測れないものを測る数学の知恵 : set

小谷元子

平成基礎科学財団　2011
Probabilistic approach to geometry

The Seasonal, Institute of, the Mathematical Society of Japan, 小谷元子, Hino Masanori, 熊谷隆, 日本数学会

Mathematical Society of Japan　2010

ISBN: 9784931469587
Spectral Analysis in Geometry and Number Theory

Motoko Kotani, Hisashi Naito, Tatsuya Tate

American Mathematical Society　2009/09
Spectral analysis in geometry and number theory : international conference on the occasion of Toshikazu Sunada's 60th birthday, August 6-10, 2007, Nagoya University, Nagoya, Japan

小谷元子, 内藤久資, Tate Tatsuya, 砂田利一

American Mathematical Society　2009

ISBN: 9780821842690
離散群の作用する無限グラフのスペクトル解析とグロモフ・ハウスドルフ収束

小谷元子

[小谷元子]　2008
文庫で読む科学

岩波書店編集部編

Iwanami　2007/06/06
「心は燃えていたではないか」in 文庫で読む科学

小谷元子

岩波書店岩波科学ライブラリー　2007
unscaled peaks of geometry

小谷元子, 宮岡礼子

日本評論社　2004/07

ISBN: 4535784035
Discrete geometric analysis : proceedings of the first JAMS Symposium on Discrete Geometric Analysis, December 12-20, 2002, Sendai, Japan

小谷元子, 白井朋之, 砂田利一, JAMS Symposium on, Discrete Geometric Analysis

American Mathematical Society　2004

ISBN: 0821833510
結晶格子の標準的実現と磁場付き推移作用素のスペクトル解析

小谷元子

[小谷元子]　2004
２１世紀の数学

小谷元子, 宮岡礼子

日本評論社　2004
ポストモダン解析学（訳）

ユルゲンヨスト著

シュプリンガー東京　2000/10
調和写像のバブル現象とコンパクト化理論

小谷元子

[小谷元子]　2000
ポストモダン解析学

ユルゲンヨスト著, 小谷元子訳

シュプリンガー・フェアラーク東京　2000

ISBN: 9784431708711

Show all Show first 5

Presentations 95

離散幾何解析と物質科学への応用 Invited

Motoko Kotani

The World of Mathematical Physics II　2021/11/21
DX社会の基盤技術～数理を活用した産学連携について Invited

Motoko Kotani

2021/07/16
材料探索のための離散幾何解析学 Invited

Motoko Kotani

2021/03/14
デジタル時代の数学・材料科学連携 Invited

Motoko Kotani

2020/12/04
デジタル時代の化学―数学連携 Invited

KOTANI Motoko

2020/09/26
数学でミクロとマクロをつなぐ Invited

KOTANI Motoko

2020/01/12
次世代材料探索のための数学ー材料科学連携 Invited

KOTANI Motoko

2019/12/20
Mathematical challenges for materials design Invited

KOTANI Motoko

Frontiers in Mathematical Science Research Workshop　2019/09/28
MATHEMATICAL CHALLENGES FOR MATERIALS DESIGN BASED ON DISCRETE GEOMETRIC ANALYSIS

KOTANI Motoko

2019 KWMS International Conference　2019/08/23
Non commutative geometry for Topological Phase Invited

KOTANI Motoko

In and around Topological Physics　2019/07/15
Discrete geometric analysis for materials research Invited

KOTANI Motoko

ICCM 2019　2019/06/09
Materials research in the digitalized society Invited

KOTANI Motoko

World Premier Research in Japan Symposium　2019/01/25
Mathematical challenge to understand Materials structure

KOTANI Motoko

2018 Taiwan Mathematical Society Annual Meeting　2018/12/08
Key Messages from Concurrent Sessions AI/IoT/Robotics Invited

KOTANI Motoko

STS forum Annual Meeting 2018　2018/10/09
世界レベルの研究拠点を作る：WPI-AIMRの活動 Invited

KOTANI Motoko

Science Japan Meeting 2019-日本の科学の未来を創る-　2018/09/20
数学と諸分野・産業との連携への挑戦 Invited

KOTANI Motoko

日本機械学会2019年度年次大会特別講演　2018/09/11
離散幾何学による物質探索への挑戦 Invited

KOTANI Motoko

2018/04/02
数学-材料科学連携による挑戦 Invited

KOTANI Motoko

第18回豊田理研懇話会　2018/01/16
Mathematical challenges for materials design International-presentation Invited

KOTANI Motoko

Total Energy and Force Methods 2018 Workshop　2018/01/10
AIMR's challenge based on Mathematics and Materials collaboration International-presentation Invited

KOTANI Motoko

Tsinghua-Tohoku Joint Workshop on Material and Spintronics Sciences　2017/12/21
Mathematical challenge for materials science International-presentation Invited

KOTANI Motoko

2017 Dasan Conference Mathematical Challenges and Industrial Problem Solving　2017/12/02
数学から材料科学へのアプローチ Invited

KOTANI Motoko

シンポジウム「高分子未来サミット」　2017/11/27
次世代物質う探索のための離散幾何学領域紹介 Invited

KOTANI Motoko

第11回物性科学領域横断研究会（領域合同研究会　2017/11/18
Discrete surface theory for trivalent graphs and its application to materials science International-presentation Invited

KOTANI Motoko

Geometry Workshop in Obergurgl 2017　2017/09/23
Mathematical Challenge to Understanding of Material International-presentation Invited

KOTANI Motoko

International Conference on Research and Education in Mathematics 2017 (ICREM8)　2017/08/12
数学は美しい〜数学が持つ力と可能性 Invited

KOTANI Motoko

経営ビジョン構想懇話会　2017/06/20
Structure understanding of materials by discrete geometric analysis International-presentation Invited

KOTANI Motoko

International Workshop on Industrial Mathematics　2017/05/19
数学による構造・機能相関の解明

17-1ポリマーフロンティア21　2017/04/01
Structure understanding of materials by discrete geometric analysis International-presentation Invited

Novel Optical Materials　2017/03/16
Structure understanding of materials by discrete geometric analysis International-presentation Invited

Stochastic Analysis and Large Scale Interacting Systems　2017/03/10
A challenge to a new paradigm by math-mate collaboration at AIMR

第14回I?CNERセミナー・シリーズ　2016/11/16
異分野融合への挑戦

第８回九州・沖縄アイランド女性研究者支援シンポジウムin沖縄　2016/11/11
A mathematical challenge to materials International-presentation Invited

GEMS 2017　2016/10/17
Topology in Materials International-presentation Invited

Topological matter, strings, K-theory and related areas　2016/09/26
数学と材料科学の連携のもたらす未来―東北大学原子分子材料科学高等研究機構（AIMR）における実験― Invited

俯瞰ワークショップナノテクノロジー・材料分野領域別分科会全体会議「研究開発力強化に向けた施策間連携」　2016/08/22
Structure understanding of materials by discrete geometric analysis International-presentation Invited

2016居禮夫人高中化學營　2016/07/14
Mathematical challenge for materials research at AIMR International-presentation Invited

International Conference on Mathematics and Mathematics Education (ICMME) 2016　2016/07/13
Mathematical Challenge to a New Phase of Materials Science International-presentation Invited

Workshop on nonlinear partial differential equations and related topics　2016/05/09
Mathematical challenge to structural understanding of materials International-presentation Invited

2nd International Symposium on Frontiers in Materials Science (FMS)　2015/11
データ社会の材料開発と数学の役割 Invited

JST CREST-さきがけ数学シンポジウム 2015『22 世紀社会創造のための数学』　2015/09
Mathematical challenge to structural understanding and structure of materials International-presentation Invited

15th International Conference Computational and Mathematical Methods in Science and Engineering　2015/07
Mathematical Challenge to Structural Understanding of Materials International-presentation Invited

Mathematics of Novel Materials　2015/06
Mathematical challenge to structural understanding of materials International-presentation Invited

2015 East Asian Core Doctorial Forum on Mathematics　2015/01
Structural Understanding of Materials-Collaboration Between Mathematics and Materials Science International-presentation Invited

150 years of beautiful structures and defects　2014/11
Discrete geometric analysis applied to structural understanding of materials International-presentation Invited

Inverse Problems and Spectral Theory　2014/10
Dynamics of mesoscopic structure in laser-induced phase separation studied by nano-second time-resolved light scattering and structured illumination microscopy

豊内秀一, 梶本真司, 戸田昌利, 赤間陽二, 川勝年洋, 小谷元子, 福村裕史

The 8th annual Meeting of Japan Society for Molecular Science　2014/09/22
Discrete Geometric Analysis applied to structural understanding of Materials International-presentation Invited

Canberra - Japan Meeting, Pattern Formation: Mathematics and Materials　2014/04/29
Discrete Geometric Analysis applied to structural understanding of Materials International-presentation

The Fourth Conference of Tsinghua Sanya International Mathematics Forum　2013/12
Discrete Geometric Analysis applied to structural understanding of Materials International-presentation Invited

Tohoku University Forum at UCL　2013/11/21
Discrete Geometric Analysis applied to structural understanding of Materials International-presentation

CAMP opening symposium　2013/11
Discrete Geometric Analysis applied to structural understanding of Materials International-presentation

HeKKSaGOn University Consortium The 3rd Japanese-German University President's Conference　2013/09/11
Discrete Geometric Analysis applied to structural understanding of Materials, A mathematical challenge to a new phase of materials science International-presentation

Connections 2013 Symposium: Crossing Boundaries with Informatics ? from Basic Science to Social Infrastructure　2013/07/08
Discrete Geometric Analysis applied to structural understanding of Materials International-presentation

Joint International Meeting of the AMS and the Romanian Mathematical Society　2013/06/27
Discrete Geometric Analysis applied to structural understanding of Materials International-presentation

10th France-Japan Workshop on Nanomaterials - The 1st WPI workshop on materials science　2013/06
Mathematical challenge to a new phase of materials science based on discrete geometric analysis International-presentation

Motoko Kotani, A. Hirata, L. J. Kang, T. Fujita, B. Klumov, K. Matsue, A. R. Yavari, M. W. Chen

Joint International Meeting of the AMS and the Romanian Mathematical Society　2013/06
A mathematical challenge to materials science International-presentation

Workshop on Stochastic Analysis and Related Topics　2012/11/08
A mathematical challenge to materials science International-presentation

The Seventh General Meeting of Asian Consortium on Computational Materials Science-Virtual Organization　2012/11
A mathematical challenge to materials science

第18回複素幾何シンポジウム　2012/10
A mathematical challenge to materials science

RIMS研究集会「Discrete Geometric Analysis」　2012/08
A mathematical challenge to materials science

理研研究会「物質科学の数学的手法と数理物理」　2012/06
A mathematical challenge to materials science International-presentation

Topology and Functional Analysis 2012　2012/05
Geometry and Analysis International-presentation

International Conference “Geometry and Analysis”　2009/12/21
Geometry of crystal lattices International-presentation

Series of Lectures　2009/11/01
Mathematical challenge to a new phase of material sciences International-presentation

Workshop “Boundaries”　2009/07/01
A mathematical challenge to material sciences International-presentation

Collocium Talk,,Technische Universität Graz　2009/03/23
A mathematical challenge to material sciences International-presentation

Colloqium talk　2009/03/18
Geometric aspect of random walk on a crystal lattice, International-presentation

Algebras, Operators and Noncommutative Geometry,　2008/12/01
Geometric aspect of random walk on a crystal lattice International-presentation

Perspectives in mathematical sciences　2008/10/08
geometric Aspects of Random Walks on a Crystal Lattice International-presentation

France-Japan Science Forum　2008/10/07
geometric Aspects of Random Walks on a Crystal Lattice International-presentation

Korea Women Mathemarics　2008/06/16
geometric Aspects of Random Walks on a Crystal Lattice International-presentation

Noncommutative Geometry　2008/02/21
geometric Aspects of Random Walks on a Crystal Lattice International-presentation

Expanders in pure and applied mathematics　2008/02/11
geometric Aspects of Random Walks on a Crystal Lattice International-presentation

The 6th 21st COE Symposium, Exploring New Science by Bridging Particle-Matter Hierarchy　2007/12/13
geometric Aspects of Random Walks on a Crystal Lattice International-presentation

Stochastic calculus on manifolds, graphsm adn random structures　2007/10/08
Geometric Aspects of Random Walks on a Crystal Lattice International-presentation

KIAS conference on Geometric Analysis　2007/09/07
Geometric Aspects of Random Walks on a Crystal Lattice International-presentation

Analysis on graphs and fractals　2007/05/29
Geometric aspects of random walks on a crystal lattice International-presentation

Stochastic Models and DiscreteGeometry　2007/02/26
Magnetic transition operators on a crystal lattice International-presentation

Noncommutative Geometry 2006 Kyoto　2006/06/13
Random walks and Geometry of a crystall lattice International-presentation

Quantum Probability and Spectral Analysis on Large Graphs　2004/09/19
Magnetic transition operators on a crystal lattice International-presentation

Geometric Group Theory, Random Walks, and Harmonic Analysis　2004/06/13
Electron transport on a crystal lattice with and without magnetic field International-presentation

The 21st century COE program of Tohoku university,International Symposium　2004/03/04
Magnetic transition operators on a crystal lattice International-presentation

Geometry and spectral theory　2003/12/29
magnetic transition operators on a crystal lattice International-presentation

minisymposium on spectral geometry　2003/10/17
Magnetic transition operators on a crystal lattice

確率論と幾何解析　2003/09/16
Magnetic transition operators on a crystal lattice International-presentation

Potential Theory and Analysis on Metric Space　2003/06/30
Geometrical aspect of large deviation for random walks on a crystal lattice International-presentation

The First JAMS Symposium, Matsusima　2002/12/12
結晶格子の磁場付き推移作用素のスペクトル端のリプシッツ連続性

作用素論，作用素環論研究集会　2002/10/30
結晶格子のランダム・ウォークの大偏差と空間の収束 I, II(連続講演）

代数的組み合わせ論シンポジウム　2002/07/01
結晶格子のランダム・ウォークの大偏差と空間の収束 I, II(連続講演）

微分幾何研究集会　2002/02/21
結晶格子の収束と大偏差

Sendai Submanifolds Day　2002/02/19
結晶格子上のランダム・ウォークと結晶格子の幾何

第２２回Encounter with Mathematics　2002/02/12
A central limit theorem for magnetic transition operators on a crystallattice International-presentation

International Centre for Mathematical Sciences　2001/07/09
A central limit theorem for magnetic transition operators on a crystallattice International-presentation

Geometry in Large　2001/06/11
A central limit theorem for magnetic transition operators on a crystallattice International-presentation

Random walks and statistical Physics　2001/02/19
結晶格子のスペクトル幾何学I,II

幾何シンポジウム　2000/07/31

Show all Show first 5

Other 2

離散幾何学から提案する新物質創成・物性発現の解明

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ミクロな幾何構造がマクロな現象を制御する仕組みを離散幾何解析学の立場で理解する
Spectral Analysis of magnetic transition operators via C* algebra

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磁場付き推移作用素をC*環の元とみることで，スペクトル集合の代数的構造や，自己相似性を解析する．