Updated on 2025/05/21

写真a

 
MURAYAMA TAKUYA
 
Organization
Faculty of Mathematics Division of Analysis Assistant Professor
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）
Title
Assistant Professor
Contact information
メールアドレス
Profile
Many "critical phenomena", important in statistical physics and probability theory, are conjectured or already known to be conformally invariant. In two dimension, this invariance can be regarded as the invariance under conformal mappings in complex analysis. "Schramm-Loewner evolution" (SLE) was introduced as a stochastic process which has such a conformal invariance. SLE is the random time-evolution of a family of conformal mappings; in view of complex analysis, it is described by the Loewner differential equation. This equation was originally employed to prove the Bieberbach conjecture, but there are many other possible applications in physics and mathematics, including SLE, integrable systems, Hele-Shaw flow, and non-commutative probability. Under these backgrounds, I'm studying SLE and the Loewner equation from both probabilistic and complex-analytic points of view.
External link

Research Areas

  • Natural Science / Basic analysis

Degree

  • Doctor of Science, Kyoto University

Research History

  • 中央大学理工学部物理学科　学振特別研究員PD，2021年4月～2022年3月   

Education

  • Kyoto University   Graduate School of Science   Division of Mathematics and Mathematical Sciences

    2018.4 - 2021.3

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    Country：Japan

    Notes：doctor program

  • Kyoto University   Graduate School of Science   Division of Mathematics and Mathematical Sciences

    2016.4 - 2018.3

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    Country：Japan

    Notes：master course

  • Kyoto University   Faculty of Science   School of Science

    2012.4 - 2016.3

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    Country：Japan

Research Interests・Research Keywords

  • Research theme： Loewner equation and Schramm-Loewner evolution on multiply connected domains

    Keyword： stochastic analysis, geometric function theory, Schramm-Loewner evolution, multiply connected domain, Komatu-Loewner equation, Brownian motion with darning

    Research period： 2022.4

Awards

  • 井上研究奨励賞

    2024.2   井上科学振興財団   平行截線半平面上のレヴナー鎖および発展族

  • 建部賢弘奨励賞

    2023.9   日本数学会   MSJ Takebe Katahiro Prize for Encouragement of Young Researchers

Papers

  • Loewner chains and evolution families on parallel slit half-planes Reviewed International journal

    Takuya Murayama

    Journal of Mathematical Analysis and Applications   526 ( 1 )   2023.3   （ ISSN:0022-247X eISSN:1096-0813 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    In this paper, we define and study Loewner chains and evolution families on finitely multiply-connected domains in the complex plane. These chains and families consist of conformal mappings on parallel slit half-planes and have one and two “time” parameters, respectively. By analogy with the case of simply connected domains, we develop a general theory of Loewner chains and evolution families on multiply connected domains and, in particular, prove that they obey the chordal Komatu–Loewner differential equations driven by measure-valued processes. Our method involves Brownian motion with darning, as do some recent studies.

    DOI： 10.1016/j.jmaa.2023.127180

    Web of Science

    Scopus

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    Repository Public URL： https://hdl.handle.net/2324/7173554

  • On the continuity of half-plane capacity with respect to Carathéodory convergence Invited Reviewed International journal

    Takuya Murayama

    Springer Proceedings in Mathematics & Statistics   394   379 - 399   2022.8   （ ISSN:2194-1009 ISBN:978-981-19-4671-4 eISSN:2194-1017 ）

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Nature Singapore  

    We study the continuity of half-plane capacity as a function of boundary hulls with respect to the Carathéodory convergence. In particular, our interest lies in the case that hulls are unbounded. Under the assumption that every hull is contained in a fixed hull with finite imaginary part and finite half-plane capacity, we show that the half-plane capacity is indeed continuous. We also discuss the extension of this result to the case that the underlying domain is finitely connected.

    DOI： 10.1007/978-981-19-4672-1_20

    Web of Science

    Scopus

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    Repository Public URL： https://hdl.handle.net/2324/7178587

  • 平行截線半平面上のレヴナー鎖および発展族

    村山 拓也

    2021.3

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    Language：Others  

    Loewner chains and evolution families on parallel slit half-planes

    DOI： 10.14989/doctor.k22977

  • Univalence and holomorphic extension of the solution to ω-controlled Loewner–Kufarev equations Reviewed International journal

    Takafumi Amaba, Roland Friedrich, Takuya Murayama

    Journal of Differential Equations   269 ( 3 )   2697 - 2704   2020.7

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    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.jde.2020.02.011

  • On the slit motion obeying chordal Komatu–Loewner equation with finite explosion time Reviewed International journal

    Takuya Murayama

    Journal of Evolution Equations   20 ( 1 )   233 - 255   2020.3

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    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/s00028-019-00519-3

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Books

  • Stochastic Komatu-Loewner Evolutions International journal

    Zhen-Qing Chen, Masatoshi Fukushima, Takuya Murayama（Role：Joint author）

    World Scientific  2023.2    （ ISBN:9789811262784 ）

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    Total pages：xv, 238 p.   Responsible for pages：256 pages.   Language：Japanese   Book type：Scholarly book

    The present monograph on stochastic Komatu–Loewner evolutions (SKLEs) provides the first systematic extension of the Schramm–Loewner evolution (SLE) theory from a simply connected planar domain to multiply connected domains by using the Brownian motion with darning (BMD) that has arisen in a recent study of the boundary theory of symmetric Markov processes. This volume is presented in an accessible manner for the interested researchers and graduate students. It also brings new insights into SLEs as special cases of SKLEs. Mathematically, it can be viewed as a powerful application of stochastic analysis via BMDs to complex analysis.

    DOI： 10.1142/13038

    Scopus

    CiNii Books

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Presentations

  • multi-finger Loewner微分方程式とmultiple SLEに対する時間変更の方法 Invited

    村山拓也

    福岡複素解析シンポジウム  2024.3 

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    Event date： 2024.3

    Language：Japanese  

    Venue：九州大学   Country：Japan  

  • Additive processes on the real line and Loewner chains

    村山拓也

    新潟確率論ワークショップ  2024.3 

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    Event date： 2024.3

    Language：Japanese  

    Venue：新潟大学   Country：Japan  

  • Notes on locally uniform weak convergence with application to additive processes

    村山拓也

    マルコフ過程とその周辺  2024.2 

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    Event date： 2024.2

    Language：Japanese  

    Venue：鹿児島県鹿児島市 天文館ビジョンホール   Country：Japan  

  • Notes on locally uniform weak convergence with application to additive processes

    村山拓也

    無限分解可能過程に関連する諸問題  2024.2 

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    Event date： 2024.2

    Language：Japanese  

    Venue：統計数理研究所   Country：Japan  

  • multi-finger Loewner微分方程式とmultiple SLEに対する時間変更の方法 Invited

    村山拓也

    関西大学確率論研究会2024  2024.2 

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    Event date： 2024.2

    Language：Japanese  

    Venue：関西大学梅田キャンパス   Country：Japan  

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MISC

  • 確率論と複素解析　～SLE, Loewner方程式が見せる多様な側面～

    村山拓也

    数理科学，サイエンス社   2022.7

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    Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

    Repository Public URL： https://hdl.handle.net/2324/7178588

  • Loewner chains and evolution families on parallel slit half-planes

    村山 拓也

    第11回白浜研究集会 報告集   2020.2

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    Language：Others  

Professional Memberships

  • The Mathematical Society of Japan

Academic Activities

  • International Workshop on Conformal Dynamics and Loewner Theory 2025 International contribution

    Role(s)： Planning, management, etc.

    Ikkei Hotta, Takuya Murayama  2025.1

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    Type：Academic society, research group, etc. 

  • 「等角写像論・値分布論」合同研究集会

    Role(s)： Planning, management, etc.

    柳原宏，須川敏幸，藤解和也，石崎克也  （ Japan ） 2024.2

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    Type：Competition, symposium, etc. 

  • 第2回数理新人セミナー

    Role(s)： Planning, management, etc.

    鷲見拳，伊藤和広，角濱寛隆，武田渉，田代賢志郎，長岡高広，村山拓也  （ Japan ） 2019.2

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    Type：Competition, symposium, etc. 

Research Projects

  • レヴナーの方法に基づく平面ツリーの確率解析・幾何

    Grant number：24K16935  2024.4 - 2029.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Early-Career Scientists

    村山 拓也

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    Grant type：Scientific research funding

    本研究の主題は，ランダムツリーをはじめとする複雑な弧状・樹状集合を平面に埋め込む一つの方法である．その方法は，複素解析で知られたレヴナー微分方程式に基づく．この方程式により，例えばランダムツリーの情報をランダムな1次元粒子系に「書き込む」ことができる．反対に，粒子系の情報を「読み出し」て，平面上に樹状集合を実現することもできる．こうした対応によって，確率論や数理物理に現れる複雑な平面集合に対し，新たな解析手法を提供することを目指す．

    CiNii Research

  • Loewner equation and Teichmueller space theory

    Grant number：23K25775  2023.4 - 2028.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    松崎 克彦, 新井 仁之, 小森 洋平, 須川 敏幸, 堀田 一敬, 柳下 剛広, 村山 拓也

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    Grant type：Scientific research funding

    普遍タイヒミュラー空間は，円周の変形のパラメーター空間とみなせる．変形の仕方や出来上がった像に対する制約が，対応する部分空間を定める．また，ある曲線から別の曲線への最も効率のよい変形は，その部分空間に与える計量で表現できる．このような円周の変形をそれが載っている平面全体の変形として表すためには，円周上の写像を無駄なく平面上に拡張する方法が必要になる．そのような拡張の方法は，これまでにも研究されてきたが，この課題ではレブナー方程式から定義される写像に注目する．レブナー方程式は，平面領域が時間発展して動いていくときに，その時間パラメーターと領域への写像の関係を記述する微分方程式である．

    CiNii Research

  • Construction of cross-sectional theory on those conformally invariant random fields which extend SLE

    Grant number：22K20341  2022 - 2023

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Research Activity start-up

    Murayama Takuya

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    Authorship：Principal investigator  Grant type：Scientific research funding

    Aiming at deep analysis of Schramm-Loewner evolution (SLE), we implemented research from perspectives of probability theory and complex analysis. Our main interest was how to extend the mathematical definition of SLE from simply connected planar domains to more general domains. In that direction, we published a book with two co-authors and made the foundation of our study clearer and solider. In another direction, we made effort to increase opportunities of research communication and, as a result, recognized new applications and problems on the Loewner differential equations.

    CiNii Research

  • 多重連結領域上のSLEと共形不変な確率場および臨界現象の解明

    Grant number：21J00656  2021

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for JSPS Fellows

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    Grant type：Scientific research funding

  • New developments in stochastic analysis

    Grant number：23K20216  2020.4 - 2025.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    稲浜 譲, 星野 壮登, 村山 拓也

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    Grant type：Scientific research funding

    伊藤清が発明した確率微分方程式をいわば「決定論化」したのが、ラフパス理論である。確率微分方程式と言う確率論の文字通り中心にある。重要な研究対象物を全く違う角度から見る新しい理論である。またラフパス理論の考え方を確率偏微分方程式に適用してできたのが「特異な確率偏微分方程式」理論である。この理論により今まで解けていなかった確率偏微分方程式が系統的に解けるようになった。本研究はこれらの新しくて重要な話題を進展させることを目指す。

    CiNii Research

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Educational Activities

  • 主に，理学部数学科の演習科目を担当しています．

Class subject

  • 統計数学・演習

    2023.10 - 2024.3   Second semester

  • 情報統計学演習

    2023.10 - 2024.3   Second semester

  • 情報解析学演習

    2023.10 - 2024.3   Second semester

  • 数学概論IV・演習

    2023.10 - 2024.3   Second semester

  • 統計数学・演習

    2022.10 - 2023.3   Second semester

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FD Participation

  • 2022.4   Role：Participation   Title：令和４年度 第１回全学ＦＤ（新任教員の研修）The 1st All-University FD (training for new faculty members) in FY2022

    Organizer：University-wide

  • 2022.4   Role：Participation   Title：数理学府FD

    Organizer：[Undergraduate school/graduate school/graduate faculty]