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
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
ORCID
Degree
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Doctor of Science, Kyoto University
Research History
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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
Research Interests・Research Keywords
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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
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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
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建部賢弘奨励賞
2023.9 日本数学会 小松・レヴナー発展の研究
Papers
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Loewner chains and evolution families on parallel slit half-planes Reviewed International journal
Takuya Murayama
Journal of Mathematical Analysis and Applications 526 2023.3
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On the continuity of half-plane capacity with respect to Carathéodory convergence Invited Reviewed International journal
394 379 - 399 2022.8
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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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Univalence and holomorphic extension of the solution to ω-controlled Loewner–Kufarev equations Reviewed International journal
269 ( 3 ) 2697 - 2704 2020.7
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On the slit motion obeying chordal Komatu–Loewner equation with finite explosion time Reviewed International journal
20 ( 1 ) 233 - 255 2020.3
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Chordal Komatu–Loewner equation for a family of continuously growing hulls Reviewed International journal
129 ( 8 ) 2968 - 2990 2019.8
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Chordal Komatu-Loewner equation for a family of continuously growing hulls
2018.3
Books
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Stochastic Komatu-Loewner Evolutions
Zhen-Qing Chen, Masatoshi Fukushima, Takuya Murayama（ Role： Joint author）
World Scientific 2023.2
Presentations
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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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Additive processes on the real line and Loewner chains
2024.3
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Notes on locally uniform weak convergence with application to additive processes
2024.2
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Notes on locally uniform weak convergence with application to additive processes
2024.2
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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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Some recent results on chordal Komatu-Loewner equation Invited International conference
Takuya Murayama
Geometric Function Theory in Several Complex Variables and Complex Banach Spaces 2023.12
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非可換Lévy過程・加法過程と正則函数の半群・Loewner鎖
村山拓也
ランダム行列と自由確率論 workshop 2023 2023.11
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Loewner chains and evolution families on parallel slit half-planes International conference
Takuya Murayama
Stochastic Processes and Related Fields 2023.8
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Loewner chains and evolution families on parallel slit half-planes Invited
2022.12
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加法過程の分布の時刻に関する広義一様弱収束 Invited
村山拓也
大規模相互作用系の確率解析 2022.12
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Locally uniform weak convergence in time of the distributions of additive processes
2022.11
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Loewner方程式について
村山拓也
第56回函数論サマーセミナー 2022.9
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On the continuity of half-plane capacity with respect to Carath\'eodory convergence Invited International conference
Takuya Murayama
International Workshop on Dirichlet Forms and Related Topics 2022.8
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On the continuity of half-plane capacity with respect to Carath'eodory convergence Invited
Riemann surfaces and related topics -In memory of Professor Yoichi Imayoshi 2022.2
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On the continuity of half-plane capacity with respect to Carath'eodory convergence Invited
Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2022 2022.1
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On the continuity of half-plane capacity with respect to Carath'eodory convergence Invited
2021.11
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On the continuity of half-plane capacity with respect to Carath'eodory convergence
2021.9
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On the continuity of half-plane capacity with respect to Carath'eodory convergence
2021.8
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複素上半平面上のchordal Loewner chainについて
村山 拓也
山口大学オンラインセミナー 2020.11
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Loewner chains and evolution families on parallel slit half-planes
2020.2
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Loewner chains and evolution families on parallel slit half-planes
2019.12
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Loewner chains and evolution families on parallel slit half-planes
2019.12
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Loewner chains and evolution families on parallel slit half-planes
2019.9
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Loewner chains and evolution families on parallel slit half-planes
2019.8
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Loewner chains and evolution families on parallel slit half-planes
2019.8
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Chordal Komatu-Loewner equation for a family of continuously growing hulls
2018.9
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Chordal Komatu-Loewner equation for a family of continuously growing hulls
2018.8
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SLEとコード型小松・Loewner（レヴナー）方程式
村山 拓也
確率論ヤングサマーセミナー 2018.8
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Characterization of the explosion time for the Komatu-Loewner evolution
2018.3
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Characterization of the explosion time for the Komatu-Loewner evolution
2017.12
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Characterization of the explosion time for the Komatu-Loewner evolution
2017.10
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An explosion problem for moduli diffusions driving stochastic Komatu-Loewner evolution
2017.8
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Characterization of the explosion time for the Komatu-Loewner evolution
2018.1
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連続なhullに対する小松・Loewner方程式とその応用について
村山 拓也
関西確率論セミナー 2018.4
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Chordal Komatu-Loewner equation for a family of continuously growing hulls
2018.5
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Chordal Komatu-Loewner equation for a family of continuously growing hulls
2019.1
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Loewner chains and evolution families on parallel slit half-planes
2019.12
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Loewner chains and evolution families on parallel slit half-planes
2020.1
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小松・Loewner微分方程式と対応するコンパクト集合族の局所成長性
村山 拓也
数学・数理科学専攻若手研究者のための異分野・異業種研究交流会 2020.10
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Some recent results on chordal Komatu-Loewner equation Invited
One-day workshop on Applied and Computational Complex Analysis (ACCA 2021) 2021.6
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On the continuity of half-plane capacity with respect to Carath'eodory convergence
2021.6
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On the continuity of half-plane capacity with respect to Carath'eodory convergence Invited
2022.1
MISC
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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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Loewner chains and evolution families on parallel slit half-planes
2020.2
Professional Memberships
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The Mathematical Society of Japan
Academic Activities
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世話人（会場係）
「等角写像論・値分布論」合同研究集会 （ 九州大学 西新プラザ ） 2024.2
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運営委員
第2回数理新人セミナー （ 京都大学 ） 2019.2
Research Projects
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SLEを拡張する共形不変確率場に対する横断的理論の構築
Grant number：22K20341 2022 - 2023
日本学術振興会 科学研究費助成事業 研究活動スタート支援
Authorship：Principal investigator Grant type：Scientific research funding
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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
日本学術振興会 科学研究費助成事業 特別研究員奨励費
Grant type：Scientific research funding
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多重連結領域におけるＬｏｅｗｎｅｒ方程式とＳＬＥ理論
Grant number：19J13031 2019 - 2020
日本学術振興会 科学研究費助成事業 特別研究員奨励費
Grant type：Scientific research funding
Class subject
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統計数学・演習
2023.10 - 2024.3 Second semester
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情報統計学演習
2023.10 - 2024.3 Second semester
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情報解析学演習
2023.10 - 2024.3 Second semester
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数学概論IV・演習
2023.10 - 2024.3 Second semester
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統計数学・演習
2022.10 - 2023.3 Second semester
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数学概論Ⅳ・演習
2022.10 - 2023.3 Second semester
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情報解析学演習
2022.10 - 2023.3 Second semester
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情報統計学演習
2022.10 - 2023.3 Second semester
FD Participation
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2022.4 Role：Participation Title：数理学府FD
Organizer：[Undergraduate school/graduate school/graduate faculty]
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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