Basic Information

Faculty

• Faculty of Science

Academic Degree

• 修士（理学）(北海道大学)
• 博士（理学）(北海道大学)

Research History

• From Oct. 2022, To Present

  京都大学大学院理学研究科, 准教授
• From Oct. 2017, To Sep. 2022

  京都大学大学院理学研究科/白眉センター, 特定准教授

ID,URL

• J-Global ID

  201701011735538562

researchmap URL

• https://researchmap.jp/7000021256

Research

Research Topics, Overview of the research

• Research Topics

  My research theme is the mathematical analysis of partial differential equations that have hypersurfaces with singularities as solutions. I am interested in the existence, uniqueness and regularity of the solutions of such equations in the weak sense. Moreover I am interested in the stability of the stationary solutions and methods of constructing the solutions such as the phase field method.

• Overview of the research

  For the evolution equation of the hypersurface such as the mean curvature flow equation, the following problem is addressed: (1) Proof of existence of a weak solution called Brakke flow, especially proof that an approximate solution obtained by the phase field method converges to a weak solution in the sense of Brakke flow. (2) Derivation of energy estimates such as Huisken's monotonicity formula of the mean curvature flow on the obtained solutions. (3) Problems of the surface evolution equations with the conservation law such as volume preservation conditions. (4) Boundary value problem for the Brakke flow such as the dynamic boundary condition.

Research Interests

• Partial differential equation, Mean curvature flow, calculus of variations, phase field method

Research Areas

• Natural sciences, Mathematical analysis

Papers

• Long time behavior for a curvature flow of networks related to grain boundary motion with the effect of lattice misoriantations

  Takashi Kagaya; Masashi Mizuno; Keisuke Takasao

  ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 13 Apr. 2023

  
• The Existence of a Weak Solution to Volume Preserving Mean Curvature Flow in Higher Dimensions

  Keisuke Takasao

  Archive for Rational Mechanics and Analysis, 15 May 2023, Peer-reviewed

  Access this paper :

  
• On Obstacle Problem for Brakke's Mean Curvature Flow

  Keisuke Takasao

  SIAM Journal on Mathematical Analysis, Jan. 2021, Peer-reviewed

  Access this paper :

  
• A curve shortening equation with time-dependent mobility related to grain boundary motions

  Masashi Mizuno; Keisuke Takasao

  Interfaces and Free Boundaries, 16 Jul. 2021, Peer-reviewed

  Access this paper :

  
• A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions

  Yoshikazu Giga; Fumihiko Onoue; Keisuke Takasao

  Differential Integral Equations, Jan. 2021, Peer-reviewed

  
• Global existence and monotonicity formula for volume preserving mean curvature flow

  Keisuke Takasao

  RIMS Kôkyûroku Bessatsu, 2020, Peer-reviewed, Lead author

  
• Existence of weak solution for mean curvature flow with transport term and forcing term

  Keisuke Takasao

  Communications on Pure & Applied Analysis, 2020, Peer-reviewed, Lead author

  
• CONVERGENCE OF THE ALLEN-CAHN EQUATION WITH CONSTRAINT TO BRAKKE'S MEAN CURVATURE FLOW

  Keisuke Takasao

  ADVANCES IN DIFFERENTIAL EQUATIONS, Sep. 2017, Peer-reviewed

  
• Gradient estimates for mean curvature flow with Neumann boundary conditions

  Masashi Mizuno; Keisuke Takasao

  NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, Aug. 2017, Peer-reviewed

  
• Existence of Weak Solution for Volume-Preserving Mean Curvature Flow via Phase Field Method

  Keisuke Takasao

  INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2017, Peer-reviewed

  
• Existence and regularity of mean curvature flow with transport term in higher dimensions

  Keisuke Takasao; Yoshihiro Tonegawa

  MATHEMATISCHE ANNALEN, Apr. 2016, Peer-reviewed

  
• New approximate method for the Allen--Cahn equation with double-obstacle constraint and stability criteria for numerical simulations

  Tomoyuki Suzuki; Keisuke Takasao; Noriaki Yamazaki

  AIMS Mathematics, 2016, Peer-reviewed

  
• Remarks on numerical experiments of the Allen-Cahn equations with constraint via Yosida approximation

  Tomoyuki Suzuki; Keisuke Takasao; Noriaki Yamazaki

  Advances in Numerical Analysis, 2016, Peer-reviewed

  
• Surface evolution for Landau-Lifshitz equation and mean curvature flow with transport term

  Keisuke Takasao

  Hokkaido university, 2013, Peer-reviewed

  
• GRADIENT ESTIMATES AND EXISTENCE OF MEAN CURVATURE FLOW WITH TRANSPORT TERM

  Keisuke Takasao

  DIFFERENTIAL AND INTEGRAL EQUATIONS, Jan. 2013, Peer-reviewed

  
• Stability of travelling wave solutions for the Landau-Lifshitz

  Keisuke Takasao

  HIROSHIMA MATHEMATICAL JOURNAL, Nov. 2011, Peer-reviewed

  

Presentations

• On obstacle problem for Brakke's mean curvature flow with Neumann boundary condition

  Keisuke Takasao

  The 81st Fujihara Seminar Mathematical Aspects for Interfaces and Free Boundaries 2024, Jun. 2024

  
• Phase field method for mean curvature flow with obstacles

  Keisuke Takasao

  Geometric PDE and Applied Analysis Seminar, Jun. 2024, Invited

  
• Phase field method for Brakke’s mean curvature flow with obstacles

  Keisuke Takasao

  Workshop on diffusion type PDEs and related topics, May 2024, Invited

  
• Brakkeの平均曲率流の障害物問題

  高棹圭介

  室蘭工業大学応用解析セミナー, Feb. 2024, Invited

  
• Existence of weak solution to volume preserving mean curvature flow

  Keisuke Takasao

  NCTS-Kyoto Mathematics Symposium, Dec. 2023

  
• フェイズフィールドモデルを用いた体積保存平均曲率流の弱解の存在について

  高棹圭介

  南大阪応用数学セミナー, Nov. 2023, Invited

  
• Existence of weak solution to volume preserving mean curvature flow

  高棹圭介

  金沢解析セミナー, Nov. 2023, Invited

  
• 重み付き平均曲率流に対するフェイズフィールド法について

  高棹圭介

  研究集会「広島微分方程式研究会」, Oct. 2023, Invited

  
• Phase field method for volume preserving mean curvature flow

  高棹圭介

  第145回HMMCセミナー, Sep. 2023, Invited

  
• Monotonicity formula of Allen-Cahn equations for surface evolution equations

  Keisuke Takasao

  Analysis, Geometry and Stochastics on Metric Spaces, Sep. 2023, Invited

  
• Phase field model for volume-preserving mean curvature flow

  Keisuke Takasao

  ICIAM 2023 Tokyo, Aug. 2023, Invited

  
• Convergence of Allen-Cahn equation with non-local term to volume preserving mean curvature flow

  Keisuke Takasao

  第48回偏微分方程式論札幌シンポジウム, Aug. 2023, Invited

  
• Phase field model for volume preserving mean curvature flow

  高棹圭介

  東工大数理解析セミナー, Jul. 2023, Invited

  
• Phase field method for mean curvature flow and vanishing of discrepancy measure

  Keisuke Takasao

  RIMS 共同研究（公開型）調和解析と非線形偏微分方程式, Jul. 2023, Invited

  
• On volume preserving mean curvature flow in higher dimensions

  Keisuke Takasao

  Kyoto-CAU Joint Meeting on Nonlinear PDEs, Mar. 2023, Invited

  
• Existence of weak solution to volume preserving mean curvature flow in higher dimensions

  Keisuke Takasao

  Geometry and Analysis Seminar -- Mini Workshop 2023, Jan. 2023, Invited

  
• フェイズフィールド法を用いた体積保存平均曲率流方程式の弱解の存在について

  高棹圭介

  第13回「解析学とその周辺」＠野田, Dec. 2022, Invited

  
• 体積保存平均曲率流の弱解の時間大域存在について

  高棹圭介

  鳥取 PDE 研究集会 2022, Nov. 2022, Invited

  
• 任意の空間次元における体積保存平均曲率流方程式の弱解の存在について

  高棹圭介

  2022年度日本数学会秋季総合分科会, Sep. 2022

  
• ある非局所項付きAllen-Cahn方程式を用いた体積保存平均曲率流の存在について

  高棹圭介

  九州関数方程式セミナー, 23 Apr. 2021, Invited

  
• Phase field model for mean curvature flow with transport term and forcing term

  高棹圭介

  第4回反応拡散方程式と非線形分散型方程式の解の挙動, 17 Feb. 2021, Invited

  
• On obstacle problem for Brakke's mean curvature flow

  Keisuke Takasao

  The 22nd Northeastern Symposium on Mathematical Analysis, 15 Feb. 2021, Invited

  
• On obstacle problem for Brakke's mean curvature flow

  高棹圭介

  第10回室蘭非線形解析研究会, 08 Jan. 2021, Invited

  
• Phase field method for volume preserving mean curvature flow

  Keisuke Takasao

  Asia-Pacific Analysis and PDE Seminar, 07 Dec. 2020, Invited

  
• Existence of weak solution for mean curvature flow with forcing term

  Keisuke Takasao

  Workshop in Geometric Measure Theory and Applications, 05 Dec. 2020, Invited

  
• On obstacle problem for Brakke flow

  高棹圭介

  北海道大学偏微分方程式セミナー, 09 Oct. 2020, Invited

  
• フェイズフィールド法による外力項付き平均曲率流方程式の弱解の存在について

  高棹圭介

  日本数学会2020年度秋季総合分科会 実函数論分科会, 25 Sep. 2020, Invited

  
• フェイズフィールド法による平均曲率流の弱解の存在について

  髙棹 圭介

  談話会, 27 Nov. 2019, 京都大学数学教室、数理解析研究所, Invited

  
• Existence of weak solution for mean curvature flow with forcing term

  Keisuke Takasao

  Oberseminar Analysis in Dortmund, 18 Nov. 2019, Invited

  
• 外力項付き平均曲率流の弱解の存在について

  髙棹 圭介

  熊本大学応用解析セミナー, 02 Nov. 2019, Invited

  
• 結晶方位差を考慮した結晶粒界の発展方程式の解の存在について

  髙棹 圭介; 水野将司

  日本数学会秋季総合分科会, 18 Sep. 2019

  
• Existence of weak solution for mean curvature flow with forcing term

  Keisuke Takasao

  Kanazawa workshop: Gradient flows and related topics: analysis and applications, 10 Aug. 2019, Invited

  
• Phase field method for mean curvature flow with dynamic boundary condition

  Keisuke Takasao

  Viscosity solution approach to asymptotic problems in front propagation, dynamical system and related topics, 17 Jul. 2019, Invited

  
• 外力項付き平均曲率流方程式に対するフェイズフィールド法

  髙棹 圭介

  東北大学 応用数理解析セミナー, 04 Jul. 2019, Invited

  
• 動的境界条件付き平均曲率流方程式に対するフェイズフィールド法

  髙棹 圭介

  表面・界面ダイナミクスの数理１７, 18 Apr. 2019, Invited

  
• Phase field method for mean curvature flow with dynamic boundary condition

  Keisuke Takasao

  研究集会「数学と現象：Mathematics and Phenomena in Miyazaki 2018」, 16 Nov. 2018, Invited

  
• Convergence of Landau-Lifshitz equation to multi-phase mean curvature flow

  Keisuke Takasao

  大阪大学 微分方程式セミナー, 22 Jun. 2018, Invited

  
• 動く曲面の数学解析

  髙棹 圭介

  第146回白眉セミナー, 08 May 2018

  
• Remarks on convergence of vector-valued Allen-Cahn equation to multi-phase mean curvature flow

  Keisuke Takasao

  松山解析セミナー 2018, 02 Feb. 2018, Invited

  
• Rectifiability of varifolds in the singular limit of Allen-Cahn equation with non-local term

  Keisuke Takasao

  第13回 非線型の諸問題, 20 Sep. 2017, Invited

  
• フェイズフィールド法によるBrakkeの平均曲率流の構成

  髙棹 圭介

  応用数学勉強会2017, 23 Aug. 2017, Invited

  
• Phase field method for mean curvature flow with a non-local term

  Keisuke Takasao

  Optimal Control and PDE, 21 Jul. 2017, Invited

  
• Convergence of the Allen-Cahn equation with non-local term to the volume preserving mean curvature flow

  Keisuke Takasao

  第３７回 南大阪応用数学セミナー, 10 Jun. 2017, Invited

  
• Existence of weak solutions for mean curvature flow with a non-local term

  Keisuke Takasao

  RIMS 共同研究（公開型） 『偏微分方程式の解の形状解析』, 06 Jun. 2017, Invited

  

Awards

• 18 Sep. 2019

  The Mathematical Society of Japan, MSJ Takebe Katahiro Prise

External funds: Kakenhi

• Construction of new phase field methods for dynamical problems in the calculus of variations

  Grant-in-Aid for Early-Career Scientists

  Basic Section 12020:Mathematical analysis-related

  Kyoto University

  Keisuke Takasao

  From 01 Apr. 2020, To 31 Mar. 2024, Project Closed

  平均曲率流方程式;幾何学的測度論;フェイズフィールド法;変分問題;弱解;バリフォールド;平均曲率流;特異極限問題;障害物問題

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20K14343/
• Multifaceted studies on dynamical problems in the calculus of variations using geometric measure theory

  Grant-in-Aid for Scientific Research (A)

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

  Tokyo Institute of Technology

  Yoshihiro TONEGAWA

  From 01 Apr. 2018, To 31 Mar. 2023, Project Closed

  平均曲率流;変分問題;極小曲面;幾何学的測度論;特異点;正則性;Mean curvature flow;Calculus of variations;Geometric measure theory;Minimal surface;Geometric analysis;mean curvature flow;calculus of variations;geometric measure theory;minimal surface;geometric analysis

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18H03670/
• Analysis on existence and uniqueness of weak solution for mean curvature flow including junction

  Grant-in-Aid for Young Scientists (B)

  Kyoto University;The University of Tokyo

  Keisuke TAKASAO

  From 01 Apr. 2016, To 31 Mar. 2020, Project Closed

  平均曲率流;幾何学的測度論;フェイズフィールド法;特異極限問題;変分問題;バリフォールド;弱解;Allen-Cahn方程式;動的境界条件;極小曲面

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16K17622/
• Measure theoretic properties of phase field models for surface evolution equations

  Grant-in-Aid for Scientific Research (C)

  Basic Section 12020:Mathematical analysis-related

  Kyoto University

  高棹 圭介

  From 01 Apr. 2023, To 31 Mar. 2027, Granted

  平均曲率流;フェイズフィールド法;幾何学的測度論;変分問題;特異極限問題;バリフォールド;弱解

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23K03180/
• Canonical mean curvature flow and its application to evolution problems

  Grant-in-Aid for Scientific Research (A)

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

  Institute of Science Tokyo

  利根川 吉廣

  From 01 Apr. 2023, To 31 Mar. 2028, Granted

  mean curvature flow;evolution problem;minimal surface;phase interface

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23H00085/
• Mathematical analysis on interface motions allowing collision, rupture and coalasce

  Grant-in-Aid for Scientific Research (B)

  Basic Section 12020:Mathematical analysis-related

  The University of Tokyo

  儀我 美一

  From 01 Apr. 2024, To 31 Mar. 2028, Granted

  界面支配モデル;相場モデル;粘性解;相転移

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-24K00531/

External funds: others

• フェイズフィールド法を用いた曲面の発展方程式の解析と偏微分方程式の幾何学的特徴付け

  科学技術人材育成費補助金(卓越研究員事業)

  From 01 Oct. 2017, To 31 Mar. 2022

  代表

Education

Teaching subject(s)

• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Differential Equations B

  0541, Fall, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Differential Equations A

  0540, Spring, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Differential Equations C

  0542, Spring, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Differential Equations D

  0543, Fall, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Calculus with Exercises A

  N149, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Calculus with Exercises B

  N150, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  ILAS Seminar

  Z001, 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

  Forefront of Mathematics and Mathematical Science I

  4138, Spring, Faculty of Science, 2
• From 01 Apr. 2024, To 31 Mar. 2025

  Linear Algebra with Exercises A

  N151, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Calculus with Exercises A

  N149, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Analysis II

  3145, Fall, Faculty of Science, 4
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Differential Equations D

  0543, Fall, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Differential Equations C

  0542, Spring, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Differential Equations B

  0541, Fall, Graduate School of Science, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Seminar on Differential Equations A

  0540, Spring, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  ILAS Seminar

  Z001, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2023, To 31 Mar. 2024

  Forefront of Mathematics and Mathematical Science I

  4138, Spring, Faculty of Science, 2
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Differential Equations D

  0543, Fall, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Seminar on Differential Equations C

  0542, Spring, Graduate School of Science, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Calculus with Exercises B

  N150, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Linear Algebra with Exercises B

  N152, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Linear Algebra with Exercises A

  N151, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Analysis I

  3144, Spring, Faculty of Science, 4
• From 01 Apr. 2022, To 31 Mar. 2023

  Forefront of Mathematics and Mathematical Science II

  4139, Fall, Faculty of Science, 2
• From 01 Apr. 2022, To 31 Mar. 2023

  Linear Algebra with Exercises A

  N151, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Differential Equations B

  0541, Fall, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Differential Equations a

  0442, Spring, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Linear Algebra with Exercises B

  N152, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Differential Equations c

  0444, Spring, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Differential Equations b

  0443, Fall, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Differential Equations d

  0445, Fall, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  ILAS Seminar

  Z001, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2022, To 31 Mar. 2023

  Seminar on Differential Equations A

  0540, Spring, Graduate School of Science, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Calculus with Exercises A

  N149, Spring, Institute for Liberal Arts and Sciences, 3
• From Apr. 2018, To Mar. 2019

  Partial Differential Equations

  Spring, 理学部
• From Apr. 2018, To Mar. 2019

  Graduate Lecture in Partial Differential Equations

  Spring, 理学研究科
• From Apr. 2018, To Mar. 2019

  Calculus with Exercises A

  Spring, 全学共通科目
• From Apr. 2018, To Mar. 2019

  Calculus with Exercises B

  Fall, 全学共通科目
• From Apr. 2018, To Mar. 2019

  Linear Algebra with Exercises A

  Spring, 全学共通科目
• From Apr. 2018, To Mar. 2019

  Linear Algebra with Exercises B

  Fall, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Partial Differential Equations

  Spring, 理学部
• From Apr. 2019, To Mar. 2020

  Graduate Lecture in Partial Differential Equations

  Spring, 理学研究科
• From Apr. 2019, To Mar. 2020

  Calculus with Exercises A

  Spring, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Calculus with Exercises B

  Fall, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Linear Algebra with Exercises A

  Spring, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Linear Algebra with Exercises B

  Fall, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Calculus with Exercises B

  Fall, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Seminar on Differential Equations a

  Spring, 理学研究科
• From Apr. 2020, To Mar. 2021

  Seminar on Differential Equations b

  Fall, 理学研究科
• From Apr. 2020, To Mar. 2021

  Seminar on Differential Equations c

  Spring, 理学研究科
• From Apr. 2020, To Mar. 2021

  Seminar on Differential Equations d

  Fall, 理学研究科
• From Apr. 2020, To Mar. 2021

  Linear Algebra with Exercises A

  Spring, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Linear Algebra with Exercises B

  Fall, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Analysis I

  Spring, 理学部
• From Apr. 2021, To Mar. 2022

  Advanced Calculus I - Vector Calculus

  Spring, 全学共通科目
• From Apr. 2021, To Mar. 2022

  Calculus with Exercises A

  Spring, 全学共通科目
• From Apr. 2021, To Mar. 2022

  Seminar on Differential Equations a

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

  Seminar on Differential Equations b

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

  Seminar on Differential Equations c

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

  Seminar on Differential Equations d

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

  Forefront of Mathematics and Mathematical Science II

  Fall, 理学部
• From Apr. 2021, To Mar. 2022

  Special study course (Mathematical Science

  Year-long, 理学部
• From Apr. 2021, To Mar. 2022

  Special study course (Mathematical Science)

  Year-long, 理学部