Basic Information

Affiliated programs (koza)

• Graduate School of Science, 数学・数理解析専攻 応用数理講座, 准教授

Academic Degree

• 修士（情報学）(京都大学)
• 博士（情報学）(京都大学)

Language of Instruction

• Japanese
• English

ID,URL

• ORCID ID

  0000-0002-0284-4608

• J-Global ID

  201301080396423060

• Researcher number

  90700352

• External link

  https://www.kurims.kyoto-u.ac.jp/~nkajino/

Website(s) (URL(s))

• https://www.kurims.kyoto-u.ac.jp/~nkajino/

researchmap URL

• https://researchmap.jp/7000005709

Research

Research Topics, Overview of the research

• Research Topics

  probability theory, analysis of Laplacians and their associated diffusion processes on fractals

• Overview of the research

  I am working on probability theory, with the principal research interest in analysis of Laplacians and their associated diffusion processes on fractals, especially how analytic properties of Laplacians reflect the geometry of the fractals. The classes of fractals include the classical Euclidean self-similar fractals, self-conformal fractals appearing naturally in complex function theory such as the limit sets of Kleinian groups and the Julia sets of complex dynamical systems, and various random fractals appearing in the context of Schramm-Loewner evolution, in particular the important two-dimensional random geometry known as the Liouville quantum gravity.

Research Areas

• Natural sciences, Basic analysis

Papers

• An elementary proof that walk dimension is greater than two for Brownian motion on Sierpiński carpets

  Naotaka Kajino

  Bulletin of the London Mathematical Society, 30 Nov. 2022, Peer-reviewed

  
• On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions

  Naotaka Kajino; Mathav Murugan

  Inventiones mathematicae, 08 Nov. 2022, Peer-reviewed

  
• On Singularity of Energy Measures for Symmetric Diffusions with Full Off-Diagonal Heat Kernel Estimates II: Some Borderline Examples

  Naotaka Kajino

  Springer Proceedings in Mathematics & Statistics, 03 Sep. 2022, Peer-reviewed, Invited

  
• The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the analytic aspects

  Naotaka Kajino

  Stochastic Analysis, Random Fields and Integrable Probability — Fukuoka 2019, Advanced Studies in Pure Mathematics, Nov. 2021, Peer-reviewed, Invited

  
• On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates

  Naotaka Kajino; Mathav Murugan

  The Annals of Probability, 01 Nov. 2020, Peer-reviewed

  
• Equivalence of recurrence and Liouville property for symmetric Dirichlet forms

  Naotaka KAJINO

  Mathematical Physics and Computer Simulation, Sep. 2017, Peer-reviewed

  
• LOCALIZED UPPER BOUNDS OF HEAT KERNELS FOR DIFFUSIONS VIA A MULTIPLE DYNKIN-HUNT FORMULA

  Alexander Grigor'yan; Naotaka Kajino

  TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Feb. 2017, Peer-reviewed

  
• Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions

  Sebastian Andres; Naotaka Kajino

  PROBABILITY THEORY AND RELATED FIELDS, Dec. 2016, Peer-reviewed

  
• Log-Periodic Asymptotic Expansion of the Spectral Partition Function for Self-Similar Sets

  Naotaka Kajino

  COMMUNICATIONS IN MATHEMATICAL PHYSICS, Jun. 2014, Peer-reviewed

  
• Non-regularly varying and non-periodic oscillation of the on-diagonal heat kernels on self-similar fractals

  KAJINO Naotaka

  Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics, Contemporary Mathematics, Nov. 2013, Peer-reviewed

  
• Analysis and geometry of the measurable Riemannian structure on the Sierpi\'{n}ski gasket

  N.~Kajino

  Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I: Fractals in Pure Mathematics, Contemporary Mathematics, Nov. 2013, Peer-reviewed

  
• On-diagonal oscillation of the heat kernels on post-critically finite self-similar fractals

  Naotaka Kajino

  PROBABILITY THEORY AND RELATED FIELDS, Jun. 2013, Peer-reviewed

  
• Time changes of local Dirichlet spaces by energy measures of harmonic functions

  Naotaka Kajino

  FORUM MATHEMATICUM, Mar. 2012, Peer-reviewed

  
• Heat Kernel Asymptotics for the Measurable Riemannian Structure on the Sierpinski Gasket

  Naotaka Kajino

  POTENTIAL ANALYSIS, Jan. 2012, Peer-reviewed

  
• Remarks on non-diagonality conditions for Sierpinski carpets

  Naotaka Kajino

  Probabilistic Approach to Geometry, Advanced Studies in Pure Mathematics, Mar. 2010, Peer-reviewed

  
• Spectral asymptotics for Laplacians on self-similar sets

  Naotaka Kajino

  JOURNAL OF FUNCTIONAL ANALYSIS, Feb. 2010, Peer-reviewed

  Access this paper :

  

Misc.

• Continuity and estimates of the transition density of the Liouville Brownian motion (Symposium on Probability Theory)

  Kajino Naotaka

  RIMS Kokyuroku, Jun. 2015

  Access this misc :

  
• Sierpinski gasket上の測度論的Riemann構造に対する解析・幾何 (確率論シンポジウム)

  梶野 直孝

  数理解析研究所講究録, Jul. 2014

  Access this misc :

  
• Energy measures for diffusions on fractals: a survey

  Naotaka Kajino

  Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs, 18 Jan. 2021, Invited

  
• フラクタルの無限/有限分岐性

  Naotaka Kajino

  数学セミナー, Feb. 2020

  
• 熊谷隆氏のHumboldt 賞受賞によせて

  Naotaka KAJINO

  数学通信, May 2018

  
• Analysis on fractals

  KAJINO Naotaka

  数学セミナー, Feb. 2017

  

Presentations

• フラクタル上の拡散過程の共形変形がGauss型熱核評価を満たし得ないことについて

  梶野 直孝

  多分野交流会, 27 Mar. 2024

  
• On singularity of p-energy measures among distinct values of p for some p.-c.f. self-similar sets

  Naotaka Kajino

  Analysis on fractals and networks, and applications, 21 Mar. 2024, Invited

  
• On singularity of p-energy measures among distinct values of p for some p.-c.f. self-similar sets

  Naotaka Kajino

  Seminaire de Probabilites commun ICJ/UMPA, 14 Mar. 2024, Invited

  
• Geometric Laplacians on self-conformal fractal curves in the plane

  Naotaka Kajino

  French Japanese Conference on Probability & Interactions, 08 Mar. 2024, Invited

  
• On singularity of p-energy measures among distinct values of p for some p.-c.f. self-similar sets

  Naotaka Kajino

  UBC Probability Seminar, 14 Feb. 2024, Invited

  
• Sharp Hoelder regularity estimates of harmonic functions for p-resistance forms

  梶野 直孝

  無限粒子系、確率場の諸問題 XVIII, 20 Jan. 2024

  
• On singularity of p-energy measures among distinct values of p on some p.-c.f. self-similar sets

  梶野 直孝

  2023年度確率論シンポジウム, 26 Dec. 2023

  
• Geometric Laplacians on self-conformal fractal curves in the plane

  Naotaka Kajino

  Random Interacting Systems, Scaling Limits, and Universality - Week 3: Workshop on Random Interacting Systems, 21 Dec. 2023, Invited

  
• 共形walk次元:値の普遍性，および高次元Sierpinski gasketと2次元Sierpinski carpetsにおける達成不可能性

  梶野 直孝

  九州確率論セミナー, 08 Dec. 2023, Invited

  
• 共形walk次元:値の普遍性，および高次元Sierpinski gasketと2次元Sierpinski carpetsにおける達成不可能性

  梶野 直孝

  神戸大学解析セミナー, 31 Oct. 2023, Invited

  
• Impossibility of quasisymmetric Gaussian uniformization, via decay rates of harmonic functions, for Brownian motion on some planar Sierpinski carpets

  Naotaka Kajino

  RIMS Symposium ``Analysis, Geometry and Stochastics on Metric Spaces'', 26 Sep. 2023, Invited

  
• Energy measures on fractals: old results and recent progress

  Naotaka Kajino

  RIMS Symposium ``Stochastic Processes and Related Fields'', 08 Sep. 2023, Invited

  
• Two-sided bounds on tail probabilities of the number of collisions of random walks

  Naotaka Kajino

  Seminar "Interacting Random Systems" at Weierstrass Institute for Applied Analysis and Stochastics, 06 Jul. 2023, Invited

  
• Impossibility of quasisymmetric Gaussian uniformization via decay rates of harmonic functions for Brownian motion on some planar Sierpinski carpets

  Naotaka Kajino

  11th International Conference on Stochastic Analysis and its Applications, 29 Jun. 2023, Invited

  
• Impossibility of quasisymmetric Gaussian uniformization, via decay rates of harmonic functions, for Brownian motion on some planar Sierpinski carpets

  Naotaka Kajino

  Potential theory and random walks in metric spaces, 01 Jun. 2023, Invited

  
• Impossibility of quasisymmetric Gaussian uniformization via decay rates of harmonic functions for Brownian motion on some planar Sierpinski carpets

  Naotaka Kajino

  Geometric and stochastic analysis on metric spaces, 14 Mar. 2023, Invited

  
• 1次元単純ランダムウォークとの比較によるSierpinski carpet上の調和関数の減衰評価

  梶野 直孝

  無限粒子系、確率場の諸問題XVII, 21 Jan. 2023

  
• Conformal walk dimension: its universal value and the non-attainment for the Sierpinski carpet

  Naotaka Kajino

  Smooth Functions on Rough Spaces and Fractals with Connections to Curvature Functional Inequalities, 21 Nov. 2022

  
• Quasisymmetric Gaussian uniformization is impossible for Brownian motion on the Sierpinski carpet

  Naotaka Kajino

  Heat Kernels, Stochastic Processes and Functional Inequalities, 01 Nov. 2022

  
• Quasisymmetric Gaussian uniformization is impossible for Brownian motion on the Sierpinski carpet

  Naotaka Kajino

  Open Japanese-German conference on stochastic analysis and applications, 23 Sep. 2022, Invited

  
• On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates II: Some borderline examples

  Naotaka Kajino

  2022年度日本数学会秋季総合分科会・統計数学分科会, 13 Sep. 2022

  
• Quasisymmetric Gaussian uniformization is impossible for Brownian motion on the Sierpiński carpet

  Naotaka Kajino

  International Workshop on Dirichlet Forms and Related Topics in Honor of Professor Masatoshi Fukushima's Beiju, 26 Aug. 2022, Invited

  
• On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates

  Naotaka Kajino

  7th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals, 04 Jun. 2022, Invited

  
• On the conformal walk dimension II: Non-attainment for some Sierpiński carpets

  Naotaka Kajino

  Probability Symposium 2021, 17 Dec. 2021

  
• Conformal walk dimension: its universal value and the non-attainment for the Sierpinski carpet

  Naotaka Kajino

  Pacific Workshop on Probability and Statistical Physics, 10 Dec. 2021, Invited

  
• ランダムウォークの衝突回数の末尾確率に対する上下評価

  梶野 直孝

  無限粒子系、確率場の諸問題XVI, 16 Oct. 2021

  
• An elementary proof of walk dimension being greater than two for Brownian motion on Sierpi\'{n}ski carpets

  Naotaka Kajino

  2021年度日本数学会年会・統計数学分科会（オンライン (Zoom)）, 15 Mar. 2021

  
• The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues

  Naotaka Kajino

  Topology and Dynamics Seminar at the University of Birmingham (online (zoom)), 18 Feb. 2021, Invited

  
• A bridge between elliptic and parabolic Harnack inequalities

  Naotaka Kajino; (joint work with; Mathav Murugan)

  RIMS共同研究（公開型）「2020年度確率論シンポジウム」（オンライン (Zoom)）, 24 Dec. 2020

  
• Sub-Gaussian heat kernel bounds imply singularity of energy measures

  Naotaka Kajino; (joint work with Mathav Murugan)

  International Conference: ``Bernoulli-IMS One World Symposium 2020'', 27 Aug. 2020

  
• フラクタル上のラプラシアンに対する解析学

  梶野 直孝

  名古屋大学多元数理科学研究科談話会（オンライン (Zoom)）, 25 May 2020, Invited

  
• Tail probability estimates for the collision number of recurrent random walks with on-diagonal heat kernel upper bounds

  Naotaka Kajino; (coauthor: Kosei Konishi); (coauthor: Makoto Makashima)

  研究集会「無限粒子系、確率場の諸問題XV」, 25 Jan. 2020

  
• Sub-Gaussian heat kernel bounds imply singularity of energy measures

  Naotaka Kajino; (coauthor: Mathav Murugan)

  2019年度確率論シンポジウム, 19 Dec. 2019

  
• The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues

  Naotaka Kajino

  第62回函数論シンポジウム, 03 Nov. 2019, Invited

  
• Sub-Gaussian heat kernel bounds imply singularity of energy measures

  Naotaka Kajino; (coauthor: Mathav Murugan)

  International Conference on Analysis and PDEs on Manifolds and Fractals, 26 Sep. 2019, Invited

  
• Analysis of Laplacians on fractals

  Naotaka Kajino

  第9回岐阜数理科学研究会, 10 Sep. 2019, Invited

  
• Sub-Gaussian heat kernel bounds imply singularity of energy measures

  Naotaka Kajino; (coauthor: Mathav Murugan)

  International Conference: Japanese-German Open Conference on Stochastic Analysis 2019, 06 Sep. 2019, Invited

  
• The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues

  Naotaka Kajino

  International Workshop: Research on the Theory of Random Dynamical Systems and Fractal Geometry, 31 Aug. 2019, Invited

  
• The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues

  Naotaka Kajino

  International Conference: The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI): Stochastic Analysis, Random Fields and Integrable Probability, 09 Aug. 2019, Invited

  
• The Laplacian on some round Sierpiński carpets and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  2019 年度日本数学会年会・幾何学分科会, Mar. 2019

  
• The Laplacian and Weyl's eigenvalue asymptotics on round Sierpiński carpets realized as the limit sets of certain Kleinian groups

  Naotaka KAJINO

  2018 年度「リーマン面・不連続群論」研究集会, Feb. 2019, Invited

  
• Analysis of diffusions on self-similar and round Sierpiński carpets

  Naotaka KAJINO

  International Workshop: Okayama Workshop on Stochastic Analysis 2019, Feb. 2019, Invited

  
• The Laplacian on some round Sierpiński carpets and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  2018 年度冬の力学系研究集会, Jan. 2019

  
• フラクタル上のラプラシアンに対する解析学

  Naotaka KAJINO

  日本数学会北海道支部講演会,, Dec. 2018, Invited

  
• The Laplacian on some round Sierpiński carpets and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  2018 年度確率論シンポジウム, Dec. 2018

  
• The Laplacian on some round Sierpiński carpets and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  2018 年度エルゴード理論とその周辺, Nov. 2018

  
• The Laplacian on some round Sierpiński carpets and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  Probability Theory Seminar, Nov. 2018, Invited

  
• フラクタル上のラプラシアンに対する解析学

  Naotaka KAJINO

  奈良女子大学理学部数学科談話会, Oct. 2018, Invited

  
• The Laplacian on some round Sierpiński carpets and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  International Conference: Fractal Geometry and Stochastics 6, Oct. 2018, Invited

  
• The Laplacian on some round Sierpiński carpets and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  International Conference: 9th International Conference on Stochastic Analysis and Its Applications, Sep. 2018, Invited

  
• フラクタル上の拡散過程に対する解析学

  Naotaka KAJINO

  平成30 年度確率論ヤングサマーセミナー, Aug. 2018, Invited

  
• Gauss 乗法カオスと2次元Liouville 量子重力の解析・幾何

  Naotaka KAJINO

  平成30 年度確率論ヤングサマーセミナー, Aug. 2018, Invited

  
• The Laplacian on some round Sierpiński carpets and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  International Workshop: Workshop on Stochastic Systems: their Analysis, Geometry and Perturbation, Jul. 2018, Invited

  
• The Laplacian on circle packing fractals: from Kesten's renewal theorem, via conformal dynamics, to Weyl's eigenvalue asymptotics

  Naotaka KAJINO

  International Conference: The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session: Perturbation Techniques in Stochastic Analysis and Its Applications, Jul. 2018, Invited

  
• The Laplacian on some round Sierpiński carpets and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  International Workshop: 2018 Spring Probability Workshop, Jun. 2018, Invited

  
• The Laplacian on circle packing fractals: from Kesten's renewal theorem, via conformal dynamics, to Weyl's eigenvalue asymptotics

  Naotaka KAJINO

  International Workshop: 2nd Hong Kong/Kyoto Workshop on Fractal Geometry and Related Areas, May 2018, Invited

  
• Weyl's eigenvalue asymptotics for the Laplacian on circle packing limit sets of certain Kleinian groups

  Naotaka KAJINO

  2018 年度日本数学会年会・函数論分科会, Mar. 2018

  
• 2 次元Liouville 量子重力：距離関数の存在・次元・熱核評価

  Naotaka KAJINO

  岡山-広島解析・確率論セミナー2018, Mar. 2018, Invited

  
• The Laplacian on self-conformal circle packing fractals: from ergodic theory to Weyl's eigenvalue asymptotics

  Naotaka KAJINO

  エルゴード理論とその周辺, Nov. 2017

  
• Weyl's eigenvalue asymptotics for the Laplacian on circle packing limit sets of certain Kleinian groups

  Naotaka KAJINO

  International Workshop: Potential Analysis and its Related Fields 2017, Sep. 2017, Invited

  
• Weyl's eigenvalue asymptotics for the Laplacian on circle packing limit sets of certain Kleinian groups

  Naotaka KAJINO

  International Conference: Japanese-German Open Conference on Stochastic Analysis 2017, Sep. 2017, Invited

  
• 円詰込フラクタル上のLaplacian とその固有値に対するWeyl の漸近公式

  Naotaka KAJINO

  東北大学数学教室談話会, Jul. 2017, Invited

  
• Weyl's eigenvalue asymptotics for the Laplacian on the Apollonian gasket and on circle packing limit sets of certain Kleinian groups

  Naotaka KAJINO

  6th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals, Jun. 2017, Invited

  
• The Laplacian on some finitely ramified self-conformal circle packing fractals and Weyl's asymptotics for its eigenvalues

  Naotaka KAJINO

  One day workshop on stochastic differential geometry, May 2017, Invited

  
• Weyl's eigenvalue asymptotics for the Laplacian on the Apollonian gasket and on circle packing limit sets of certain Kleinian groups

  KAJINO Naotaka

  International Workshop: Dirichlet forms and their geometry, Mar. 2017, Graduate School of Information Sciences, Tohoku University, Invited

  
• Weyl's eigenvalue asymptotics for the Laplacian on circle packing limit sets of certain Kleinian groups

  Naotaka KAJINO

  RIMS camp-style seminar: Large scale properties of partial differential equations with random coefficients, 2017, RIMS, Invited

  
• Weyl's eigenvalue asymptotics for the Laplacian on circle packing limitsets of certain Kleinian groups

  KAJINO Naotaka

  International Workshop:“Heat Kernels, Stochastic Processes and Functional Inequalities”, Dec. 2016, Mathematisches Forschungsinstitut Oberwolfach

  
• The Laplacian on the Apollonian gasket and its Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  “46th Saint-Flour Probability Summer School”, Jul. 2016

  
• The Laplacian on the Apollonian gasket and its Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  International Workshop: “Heat Kernels and Analysis on Manifolds and Fractals”, Jul. 2016, University of Bielefeld, Invited

  
• The Laplacian on the Apollonian gasket and its Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  International Conference: “ The 8th International Conference on Stochastic Analysis and Its Applications”, Jun. 2016, Beijing Institute of Technology, Invited

  
• The Laplacian on the Apollonian gasket and its Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  International Workshop: “Dynamics, Ergodic Theory and Fractals”, May 2016, Osaka University, Invited

  
• 論文紹介：H. Oh and N. A. Shah, "The asymptotic distribution of circles in the orbits ofKleinian groups" Invent. Math. 187 (2012) 1-35, およびH. Kesten, "Renewal theory for functionals of aMarkov chain with general state space", Ann. Probab. 2 (1974) 355-386

  KAJINO Naotaka

  4th Spring School on Stochastic and Geometric Analysis, Apr. 2016, Invited

  
• Open Problem: Optimal transport & L2-Wasserstein geodesics on the Apollonian gasket

  KAJINO Naotaka

  4th Spring School on Stochastic and Geometric Analysis, Apr. 2016, Invited

  
• Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula

  KAJINO Naotaka; A. Grigor'yan; 氏と

  International Workshop: “Workshop on SDEs and Stochastic Processes”, Apr. 2016, Chern Institute of Mathematics, Nankai University, Invited

  
• The Laplacian on the Apollonian gasket and its Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  International Workshop: “The 1st Hong Kong Kyoto Workshop on Fractal Geometry and Related Areas”, Mar. 2016, Invited

  
• The Laplacian on the Apollonian gasket and its Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  International Workshop: “2016 Spring Probability Workshop”, Mar. 2016, Invited

  
• The Laplacian on the Apollonian gasket and its Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  RIMS研究集会 複素力学系の深化, Dec. 2015

  
• Laplacian eigenvalue asymptotics on fractals via Kesten's renewaltheorem forfunctionals of Markov chains (Kesten [Ann. Probab.2 (1974),355--386]の論文紹介)

  KAJINO Naotaka

  無限粒子系、確率場の諸問題XI, Dec. 2015

  
• The Laplacian on the Apollonian gasket and its Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  確率論と幾何学, Nov. 2015, Invited

  
• The Laplacian on the Apollonian gasket and its Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  International Conference:“Stochastic Analysis”, Sep. 2015, Invited

  
• Apollonian gasket 上のLaplacianとそのWeyl型固有値漸近挙動

  KAJINO Naotaka

  2015年度日本数学会秋季総合分科会・函数論分科会, Sep. 2015

  
• Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula

  KAJINO Naotaka; A. Grigor'ya; 氏との

  International Conference:“Stochastic Analysis and Applications(German-Japanese bilateral research project, 2015)”, Aug. 2015, Invited

  
• Heat kernel analysis for Brownian motion of 2-dimensional Liouville quantum gravity

  KAJINO Naotaka; S. Andres氏との共同

  International Conference: “38th Conference on Stochastic Processes and their Applications”, Jul. 2015, Invited

  
• Analysis of Liouville Brownian motion:heat kernel (and averaged spectral asymptotics)

  KAJINO Naotaka; S. Andres氏との共同

  RIMS合宿型セミナー“確率解析の新展開”, Jul. 2015, Invited

  
• 多重Dynkin-Hunt公式による拡散過程の熱核の時空間限局的上方評価

  KAJINO Naotaka; A. Grigor'ya; 氏との

  神戸Workshop 格子上の確率解析とその周辺, Mar. 2015

  
• 多重Dynkin-Hunt公式による拡散過程の熱核の時空間限局的上方評価

  KAJINO Naotaka; A. Grigor'ya; 氏との

  2015年度日本数学会年会・統計数学分科会, Mar. 2015

  
• 2次元Liouville量子重力下のBrown運動に対する熱核解析

  KAJINO Naotaka; S. Andres氏との共同

  2015年度日本数学会年会・統計数学分科会, Mar. 2015, Invited

  
• Continuity and estimates of the transition density of the Liouville Brownian motion

  KAJINO Naotaka; S. Andres氏との共同

  確率論シンポジウム, Dec. 2014

  
• Liouville Brown運動の推移確率密度の連続性と評価

  KAJINO Naotaka; S. Andres氏との共同

  無限粒子系、確率場の諸問題X, Nov. 2014

  
• Spectral volume and surface measures via the Dixmier trace for local symmetric Dirichlet spaces with Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  International Workshop:Workshop on Dirichlet Forms & Stochastic Analysis 2014, Oct. 2014, Invited

  
• Continuity and estimates of the transition density of the Liouville Brownian motion

  KAJINO Naotaka; S. Andres氏との共同

  International Workshop: Dirichlet Form Theory and its Applications, Oct. 2014, Invited

  
• 点再帰的強局所対称Dirichlet空間における内部一様領域上のNeumann熱核評価

  KAJINO Naotaka; J. Lier; 氏との

  2014年度日本数学会秋季総合分科会・統計数学分科会, Sep. 2014

  
• Spectral volume and surface measures via the Dixmier trace for local Dirichlet spaces with Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  Seminars with E. Milman, Sep. 2014

  
• Localized heat kernel upper bounds for diffusions

  KAJINO Naotaka; A.\ Grigor'ya; 氏との

  Workshop: ``Swansea-Japanese Workshop on Stochastic Analysis", Sep. 2014, Invited

  
• Continuity and estimates of the transitiond ensity of the Liouville Brownian motion

  KAJINO Naotaka; S.\ Andres氏との共同

  International Workshop: ``UK-Japan Stochastic Analysis School", Sep. 2014

  
• Spectral volume and surface measures via the Dixmier trace for local Dirichlet spaces with Weyl type eigenvalue asymptotics

  KAJINO Naotaka

  International Conference:``Stochastic Processes, Analysis and Mathematical Physics", Aug. 2014, Invited

  
• Continuity and estimates of the Liouville heat kernelwith applications to spectral dimensions

  KAJINO Naotaka; S.\ Andres氏との共同

  44th Saint-Flour Probability Summer School, Jul. 2014

  
• Spectral volume measure via the Dixmier trace for Dirichlet spaces with Weyl type eigenvalue asymptotics

  KAZINO naotaka

  International Conference: ``Fractal Geometry and Stochastics V", Mar. 2014

  
• Neumann heat kernel estimates in inner uniform domains for point-recurrent strongly local Dirichlet spaces

  KAZINO naotaka

  Workshop: ``Stochastic Processes and Mathematical Finance", Feb. 2014, 関西大学, Invited

  
• 調和Sierpiński gasketにおける最短測地線の構造

  KAZINO naotaka

  確率論シンポジウム, Dec. 2013, 京都大学数理解析研究所

  
• Sierpińskigasket上の測度論的Riemann構造に対するLaplacianのWeyl型固有値漸近挙動

  KAZINO naotaka

  確率論シンポジウム, Dec. 2013, 京都大学数理解析研究所

  
• 点再帰的強局所Dirichlet空間における内部一様領域上のNeumann熱核評価

  KAZINO naotaka

  マルコフ過程とその周辺, Nov. 2013, 東北大学

  
• Geometry of the measurable Riemannian structure on the Sierpiński gasket: structure of minimal geodesics and Ricci lower unboundedness

  KAZINO naotaka

  2013年度日本数学会秋季総合分科会幾何学分科会, Sep. 2013, 日本数学会

  
• (Non-)periodic asymptotics of the heat kernel on Sierpiński carpets

  KAZINO naotaka

  2013年度日本数学会秋季総合分科会統計数学分科会, Sep. 2013, 日本数学会

  
• Periodic and non-periodic aspects of the heat kernel asymptotics on Sierpiński carpets

  KAZINO naotaka

  Dirichlet Forms and Applications: German-Japanese Meeting on Stochastic Analysis, Sep. 2013

  
• Periodic and non-periodic aspects of heat kernel asymptotics on Sierpiński carpets

  KAZINO naotaka

  Heat Kernels, Stochastic Processes and Functional Inequalities, May 2013

  
• Asymptotic behavior of Laplacian eigenvalues and heat kernels on self-similar fractals

  N.~Kajino

  ワークショップ：確率論早春セミナー, Mar. 2013, Invited

  
• Weyl's Laplacian eigenvalue asymptotics for the measurable Riemannian structure on the Sierpi\'{n}ski gasket

  N.~Kajino

  International Workshop: Interactions Between Analysis and Geometry --- Workshop I: Analysis on Metric Spaces, Mar. 2013

  
• Periodic and non-periodic aspects of the heat kernel asymptotics on Sierpi\'{n}ski carpets

  N.~Kajino

  International Conference: Advances on Fractals and Related Topics 2012, Dec. 2012

  
• Weyl's Laplacian eigenvalue asymptotics for the measurable Riemannian structure on the Sierpi\'{n}ski gasket

  N.~Kajino

  RIMS meeting: Potential Theory and its Related Fields, Sep. 2012

  
• Weyl's Laplacian eigenvalue asymptotics for the measurable Riemannian structure on the Sierpi\'{n}ski gasket

  N.~Kajino

  International Conference: 6th International Conference on Stochastic Analysis and Its Applications, Sep. 2012

  
• Weyl's Laplacian eigenvalue asymptotics for the measurable Riemannian structure on the Sierpi\'{n}ski gasket

  N.~Kajino

  Mini-Workshop: Dirichlet forms, Riemannian structures and Spectral analysis on Fractals, Jul. 2012, Invited

  
• Non-regularly varying and non-periodic oscillation of the on-diagonal heat kernels on self-similar fractals

  N.~Kajino

  Workshop: 5th Probability at Warwick Young Researchers Workshop, Jul. 2012

  
• Non-regularly varying and non-periodic oscillation of the on-diagonal heat kernels on self-similar fractals

  N.~Kajino

  Mini-Workshop: Dirichlet forms, Riemannian structures and Spectral analysis on Fractals, Jul. 2012, Invited

  
• Non-regularly varying and non-periodic oscillation of the on-diagonal heat kernels on self-similar fractals

  N.~Kajino

  International Conference: Nonlocal Operators: Analysis, Probability, Geometry and Applications, Jul. 2012

  
• On-diagonal oscillation of the heat kernels on p.c.f.~self-similar fractals

  N.~Kajino

  International Conference: 10th German Probability and Statistics Days 2012, Mar. 2012

  
• Non-regularly varying non-periodic oscillation of on-diagonal heat kernels on self-similar fractals

  N.~Kajino

  Workshop: Stochastic Analysis and its Applications, Mar. 2012

  
• On-diagonal oscillation of the heat kernels on p.c.f.~self-similar fractals

  N.~Kajino

  AMS Special Session on Fractal Geometry in Pure and Applied Mathematics (in memory of Benoit Mandelbrot), 2012 Joint Mathematics Meetings, Jan. 2012

  

Awards

• 29 Sep. 2011

  Mathematical Society of Japan, 2011年度日本数学会賞建部賢弘賞奨励賞

External funds: Kakenhi

• Study of Analysis and Geometry of complex spaces

  Grant-in-Aid for Scientific Research (B)

  Basic Section 12010:Basic analysis-related

  Kyoto University

  JUN KIGAMI

  From 01 Apr. 2021, To 31 Mar. 2024, Project Closed

  フラクタル;拡散過程;ラプラシアン;熱核

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21H00989/
• Analysis of Laplacians on fractals invariant under action of discrete groups of Moebius transformations

  Grant-in-Aid for Challenging Research (Exploratory)

  Medium-sized Section 12:Analysis, applied mathematics, and related fields

  Kyoto University;Kobe University

  Naotaka KAJINO

  From 29 Jun. 2018, To 31 Mar. 2024, Project Closed

  ラプラシアン;フラクタル;Weyl型固有値漸近挙動;Klein群の極限集合;Sierpinski carpet;自己等角フラクタル曲線;複素力学系のJulia集合;Klein群の擬等角変形;擬等角写像

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18K18720/
• Analysis and geometry of fractals and stochastic processes on them from field-transverse viewpoints

  Grant-in-Aid for Scientific Research (B)

  Basic Section 12010:Basic analysis-related

  Kyoto University;Kobe University

  Naotaka KAJINO

  From 01 Apr. 2018, To 31 Mar. 2022, Project Closed

  フラクタル上の解析学;劣ガウス型熱核評価;エネルギー測度;ウォーク次元;ランダム環境中のディレクティドポリマー;群上の調和解析;3次元ループ除去ランダムウォーク;3次元一様全域木;調和関数;乗法型確率熱方程式;曲面群;フラクタル上のポテンシャル論;フラクタル上の確率過程;Liouville Brown運動;フラクタル上の確率熱方程式;測度のマルチフラクタル解析;双曲群;ポテンシャル論;ランダム媒質中のディレクティドポリマー;自由エネルギー;フラクタル幾何学

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18H01123/
• Relation between structure of spaces and analysis

  Grant-in-Aid for Scientific Research (B)

  Kyoto University

  JUN KIGAMI

  From 01 Apr. 2017, To 31 Mar. 2020, Project Closed

  フラクタル;熱核;距離空間;力学系;Harnack 不等式;等角次元;ラプラシアン;解析学

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17H02849/
• Mathematical analysis of differential operators derived from singular geometric structures and their probabilistic counterparts

  Grant-in-Aid for Young Scientists (B)

  Kobe University

  Naotaka KAJINO

  From 01 Apr. 2015, To 31 Mar. 2019, Project Closed

  フラクタル解析;ラプラシアン;固有値漸近挙動;アポロニウスの詰め込み;円詰込フラクタル;クライン群;リウヴィルブラウン運動;劣ガウス型熱核評価;Apollonian gasket;Dirichlet形式;Liouville Brown運動;熱核;劣Gauss型評価;フラクタル;Klein群の極限集合;拡散過程;測度論的リーマン構造

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15K17554/
• Towerd analysis on metric-measure spaces-- Cheeger theory and fractals

  Grant-in-Aid for Challenging Exploratory Research

  Kyoto University

  Jun Kigami

  From 01 Apr. 2014, To 31 Mar. 2016, Project Closed

  解析学;フラクタル;測度論リーマン構造;測度・距離空間;Dirichlet form;partition;quasisymmetry;volume doubling property;測度論的リーマン構造;Dirichlet From;自己相似集合;tree;距離空間;quaisymmetry

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-26610023/
• Relation between algebra, geometry and analysis on fractals

  Grant-in-Aid for Scientific Research (B)

  Kyoto University

  Jun Kigami

  From 01 Apr. 2014, To 31 Mar. 2017, Project Closed

  フラクタル;熱核;ラプラシアン;Dirichlet form;力学系;タイリング;自己相似集合;確率過程;拡散過程;複素力学系

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-26287017/
• Stochastic analysis of Markov processes by Dirichlet forms and its applications

  Grant-in-Aid for Scientific Research (A)

  Tohoku University

  Masayoshi Takeda

  From 01 Apr. 2014, To 31 Mar. 2018, Project Closed

  対称マルコフ過程;ディリクレ形式;測度空間上の確率解析;準定常分布;エルゴード定理;測度距離空間上の幾何解析;特異空間上の拡散過程;無限次元確率解析;測度距離空間;無限次元空間上の確率解析;飛躍型マルコフ過程;ラフパス解析;マルコフ過程;幾何解析;フラクタル;測度距離空間上の解析;ファインマン・カッツの公式;特異空間上の幾何解析

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-26247008/
• Developments of geometry and analysis for measurable Riemannian structures on fractals

  Grant-in-Aid for Research Activity Start-up

  Kobe University

  Naotaka KAJINO

  From 30 Aug. 2013, To 31 Mar. 2015, Project Closed

  フラクタル解析;ディリクレ形式;ラプラシアン;固有値漸近挙動;コンヌのトレース定理;測度論的リーマン構造;アポロニウスの詰め込み;熱核;国際研究者交流（ドイツ，イギリス）;国際研究者交流（アメリカ）

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25887038/
• Randomness in number theory

  Grant-in-Aid for Scientific Research (B)

  Kobe University

  Katusi Fukuyama

  From 01 Apr. 2012, To 31 Mar. 2016, Project Closed

  確率論;一様分布;差異量;等比数列;重複対数の法則;uniform distribution;discrepancy;lacunary sequence;経験分布過程;間隙級数;一様分布論;間隙列

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-24340017/
• Analysis, geometry and their interplays on fractals and stochastic processes on them

  Grant-in-Aid for Scientific Research (B)

  Basic Section 12010:Basic analysis-related

  Kyoto University

  梶野 直孝

  From 01 Apr. 2022, To 31 Mar. 2027, Granted

  劣ガウス型熱核評価;フラクタル上のポテンシャル論;ランダムフラクタル;自己等角フラクタル;フラクタル上の確率熱方程式;2次元一般化Sierpinski carpet;（劣）ガウス型熱核評価;ランダム媒質中の確率過程;スケール極限;離散群上のランダムウォーク;調和測度;フラクタル上の確率過程

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22H01128/
• Analysis, geometry and their interplays on fractals and stochastic processes on them

  Grant-in-Aid for Scientific Research (B)

  Basic Section 12010:Basic analysis-related

  Kyoto University

  梶野 直孝

  From 01 Apr. 2022, To 31 Mar. 2027, Granted

  劣ガウス型熱核評価;フラクタル上のポテンシャル論;ランダムフラクタル;フラクタル上の確率過程;自己等角フラクタル;ポテンシャル論;（劣）ガウス型熱核評価;調和測度;反射壁拡散過程の境界へのトレース過程;フラクタル上のp-エネルギー形式;スケール極限;ランダムウォーク;フラクタル上の確率熱方程式;2次元一般化Sierpinski carpet;ランダム媒質中の確率過程;離散群上のランダムウォーク

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23K22399/

Education

Teaching subject(s)

• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Probability Theory b

  1308, Fall, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Probability Theory a

  1307, Spring, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Probability Theory d

  1310, Fall, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Probability Theory c

  1309, Spring, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Invitation to Modern Mathematics and Mathematical Sciences

  N114, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2024, To 31 Mar. 2025

  Special study course (Mathematical Science)

  5140, Year-long, Faculty of Science, 12
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Probability Theory b

  1308, Fall, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Probability Theory a

  1307, Spring, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Probability Theory d

  1310, Fall, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Probability Theory c

  1309, Spring, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Invitation to Modern Mathematics and Mathematical Sciences

  N114, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Probability Theory d

  1310, Fall, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Probability Theory c

  1309, Spring, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Probability Theory b

  1308, Fall, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Probability Theory a

  1307, Spring, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Probability Theory a

  1307, Spring, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Mathematical Statistics-E2

  N815, Fall, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2022, To 31 Mar. 2023

  Special study course (Mathematical Science)

  5140, Year-long, Faculty of Science, 12
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Probability Theory c

  1309, Spring, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Probability Theory d

  1310, Fall, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Probability Theory b

  1308, Fall, Graduate School of Science, 3
• From Apr. 2021, To Mar. 2022

  Seminar on Probability Theory a

  Spring, 理学研究科
• From Apr. 2021, To Mar. 2022

  Seminar on Probability Theory b

  Fall, 理学研究科
• From Apr. 2021, To Mar. 2022

  Seminar on Probability Theory c

  Spring, 理学研究科
• From Apr. 2021, To Mar. 2022

  Seminar on Probability Theory d

  Fall, 理学研究科

Administration

Faculty management (title, position)

• From 01 Apr. 2024, To 31 Mar. 2025

  理学研究科大学院教育教務委員会委員