Curriculum vitae（Tsuyoshi Yoneda:米田　剛）

Photo in Banff

Affiliation Graduate School of Economics, Hitotsubashi University, Professor
Address 2-1 Naka, Kunitachi, Tokyo 186-8601, Japan
(〒186-8601 東京都国立市中2-1)
Research interests Mathematical analysis on turbulence and deep learning, PDE (Navier-Stokes and Euler equations), Fourier analysis

Algebraic machine learning: Python code created by Tsuyoshi Yoneda

Algebraic machine learning code in GitHub
Please acknowledge the use of this script in any publications which make use of it.

This algebraic machine learning is based on the following mathematical result:
C. Nakayama and T. Yoneda, Universality of almost periodicity in bounded discrete time series

The strong point of this learning method is that there is no black box anymore.
This means that we can further mathematically analyze time series data from this learning model.

My talks on videos

  • Banff 2023(BIRS): Mathematical structure of machine learning
  • Hawaii 2022(MSRI): Mathematical analysis on turbulence
  • Berkeley 2019(MSRI): Illposedness on the Euler equations

    • My movies

  • spin1 (research on angular momentum)
  • spin2 (research on angular momentum)
  • almost geodesic flow
  • unilateral flow

    • Graduate Educations

  • Ph.D., Mathematical Sciences, University of Tokyo, March 2009: Thesis directed by Professor Yoshikazu Giga
  • M.S., Education, Osaka Kyoiku University, March 2006: Thesis directed by Professor Eiichi Nakai

    • Academic Positions

    1. April 2016-August 2021: Assosiate professor, Graduate School of Mathematical Sciences, University of Tokyo, (in Tokyo, Japan)
    2. April 2014-March 2016: Assosiate professor, Department of Mathematics, Tokyo Institute of Technology (in Tokyo, Japan)
    3. July 2011--March 2014: Assistant professor, Department of Mathematics, Hokkaido University (in Sapporo, Japan)
    4. September 2010--May 2011: Postdoctoral fellowship, Pacific Institute for the Mathematical Sciences (PIMS), University of Victoria (in Victoria, Canada, Mentor: Professor Slim Ibrahim)
    5. September 2009-August 2010: Postdoctoral fellowship, Institute for Mathematics and Its Applications (IMA), University of Minnesota (in Minnesota, USA, Mentor: Professor Vladimir Sverak)
    6. June 2009-August 2009: The Research Doctor of the Mathematics Department at Sungkyunkwan University (in Suwon, Korea, Mentor: Professor Dongho Chae)
    7. March 2009-May 2009: Short-term scholar, Department of Mathematics, Arizona State University (in Arizona, USA, Mentor: Professor Alex Mahalov)

    Books, Articles

    1. Zeroth-lawからみる瞬間的な渦伸長と或る定常流について, 日本流体力学会・学会誌「ながれ」第38巻・第6号，2019年
    2. 数理流体力学への招待， SGCライブラリ（サイエンス社）2020年1月
    3. 私のながれの学び方，No.9　純粋数学出身の私が乱流研究に至るまでの経緯，日本流体力学会。学会誌「ながれ」 第40巻・第4号， 2021年
    4. 微積分から学ぶ乱流，微積分と線形代数，数理科学・2022年5月号（サイエンス社）
    5. ラグランジュ座標系による乱流散逸構造の数学的洞察, Mathematical analysis of extreme dissipation in Lagrangian coordinate system, 日本流体力学会・学会誌「ながれ」2022年

    A list of publications since April 2014 (Articles in refereed journal)

    1. I.-J. Jeong, J. Na and T. Yoneda, Weakened vortex stretching effect in three scale hierarchy for the 3D Euler equations, to appear in Nonlinearity.
    2. Leandro Lichtenfelz, Taito Tauchi and Tsuyoshi Yoneda, Existence of a conjugate point in the incompressible Euler flow on a three-dimensional ellipsoid, to appear in Arnold Mathematical Journal.
    3. Tomonori Tsuruhashi and Tsuyoshi Yoneda, Microscopic expression of anomalous dissipation in Passive scalar transport, J. Math. Fluid Mech., 26 (2024) 5.
    4. C.-H. Chan, M. Czubak and T. Yoneda, The restriction problem on the ellipsoid, J. Math. Anal. Appl. 527 (2023) 127358.
    5. Yuuki Shimizu and Tsuyoshi Yoneda, Locality of vortex stretching for the 3D Euler equations, J. Math. Fluid Mech., 25 (2023), 18.
    6. Pritpal Matharu, Bartosz Protas and Tsuyoshi Yoneda, On Maximum Enstrophy Dissipation in 2D Navier-Stokes Flows in the Limit of Vanishing Viscosity, Physica D, 441 (2022), 133517.
    7. Nobu Kishimoto and Tsuyoshi Yoneda, Characterization of Three-dimensional Euler flows supported on finitely many Fourier modes, J. Math. Fluid Mech., 24 (2022), 74.
    8. Taito Tauchi and Tsuyoshi Yoneda, Arnold stability and Misiolek curvature, Monatshefte fur Mathematik, 199 (2022), 411--429.
    9. Tomonori Tsuruhashi, Susumu Goto, Sunao Oka, Tsuyoshi Yoneda, Self-similar hierarchy of coherent tubular vortices in turbulence, Phil. Trans. R. Soc., A, 380 (2022), 20210053.
    10. T. Tauchi and T. Yoneda, Existence of a conjugate point in the incompressible Euler flow on an ellipsoid, J. Math. Soc. Japan, 74 (2022), 629--653.
    11. T. D. Drivas, G. Misiolek, B. Shi and T. Yoneda, Conjugate and cut points in ideal fluid motion, Annales mathematiques du Quebec 46, (2022), 207--225.
    12. Tsuyoshi Yoneda, Susumu Goto and Tomonori Tsuruhashi, Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching, Nonlinearity 35 (2022), 1380--1401.
    13. I.-J. Jeong and T. Yoneda, Quasi-streamwise vortices and enhanced dissipation for the incompressible 3D Navier-Stokes equations, Proceedings of AMS, 150 (2022), 1279--1286.
    14. T. Tauchi and T. Yoneda, Positivity for the curvature of the diffeomorphism group corresponding to the incompressible Euler equation with Coriolis force, Prog. Theor. Exp. Phys., (2021), 210043.
    15. I.-J. Jeong and T. Yoneda, Vortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equations, Mathematische Annalen, 380, (2021) 2041--2072 .
    16. I.-J. Jeong and T. Yoneda, Enstrophy dissipation and vortex thinning for the incompressible 2D Navier-Stokes equations, Nonlinearity, 34 (2021) 1837.
    17. I.-J. Jeong and T. Yoneda, Three-dimensional Euler flow generating instantaneous vortex stretching and related zeroth law, Nagare: Journal of Japan Society of Fluid Mechanics, 39 (2020) 230--239.
    18. L. Lichtenfelz and T. Yoneda, A local instability mechanism of the Navier-Stokes flow with swirl on the no-slip flat boundary, J. Math. Fluid Mech., 21 (2019) 20.
    19. E. Nakai and T. Yoneda, New applications of Campanato spaces with variable growth condition to the Navier-Stokes equation, Hokkaido Math. J., 48 (2019) 99--140.
    20. N. Kishimoto and T. Yoneda, Global solvability of the rotating Navier-Stokes equations with fractional Laplacian in a periodic domain, Math. Ann. 372 (2018) 743--779.
    21. G. Misiolek and T. Yoneda Continuity of the solution map of the Euler equations in H\"older spaces and weak norm inflation in Besov spaces, Trans. Amer. Math. Soc. 370 (2018), 4709--4730.
    22. Y. Giga, S. Ibrahim, S. Shen and T. Yoneda, Global well posedness for a two-fluid model, Diff. and Integral Eq. 31 (2018) 187--214.
    23. N. Kishimoto and T. Yoneda, A number theoretical observation of a resonant interaction of Rossby waves, Kodai Math. J., 40 (2017) 16--20.
    24. P-Y. Hsu, H. Notsu, T. Yoneda, A local analysis of the axi-symmetric Navier-Stokes flow near a saddle point and no-slip flat boundary, J. Fluid Mech., 794 (2016) 444--459.
    25. T. Itoh, H. Miura and T. Yoneda, Remark on single exponential bound of the vorticity gradient for the two-dimensional Euler flow around a corner, J. Math. Fluid Mech., 18 (2016) 531--537.
    26. C-H. Chan, M. Czubak and T. Yoneda, An ODE for boundary layer separation on a sphere and a hyperbolic space, Physica D, 282 (2014) 34--38.

    Preprints

    1. C. Nakayama and T. Yoneda, Universality of almost periodicity in bounded discrete time series, https://arxiv.org/abs/2310.00290
    2. R. Kawasumi and T. Yoneda, Pointwise convergence of Fourier series and a deep neural network for the indicator function of d-dimensional ball, https://arxiv.org/abs/2304.08172
    3. Zhongyang Gu, Hu Xin and Tsuyoshi Yoneda, Anomalous smoothing effect on the incompressible Navier-Stokes-Fourier limit from Boltzmann with periodic velocity, https://arxiv.org/abs/2308.00363
    4. Tamaki Suematsu, Kengo Nakai, Tsuyoshi Yoneda, Daisuke Takasuka, Takuya Jinno, Yoshitaka Saiki, Hiroaki Miura, Machine learning prediction of the MJO extends beyond one month, submitted, arXiv:2301.01254
    5. Zhongyang Gu, Pritpal Matharu, Bartosz Protas, Hu Xin and Tsuyoshi Yoneda, TBA

      6. A list of publications until March 2014 (Articles in refereed journal)

      1. C-H Chan and T. Yoneda, On the stationary Navier-Stokes flow with isotropic streamlines in all latitudes on a sphere or a 2D hyperbolic space, Dynamics of PDE, 10 (2013) 209--254.
      2. S.Ibrahim and T. Yoneda, Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data, J. Math. Sci. Univ. Tokyo, 20 (2013) 1--25
      3. E. Foxall, S. Ibrahim and T. Yoneda, Streamlines concentration and application to the incompressible Navier-Stokes equations, Tohoku Math. J., 65 (2013) 273--279.
      4. D. Chae and T. Yoneda, On the Liouville theorem for the stationary Navier-Stokes equations in a critical space, J. Math. Anal. Appl., 405 (2013) 706--710.
      5. M. Yamada and T. Yoneda, Resonant interaction of Rossby waves in two-dimensional flow on a β plane, Physica D, 245 (2013) 1--7.
      6. C-H. Chan and T. Yoneda, On possible isolated blow-up phenomena and regularity criterion of the 3D Navier-Stokes equation along the streamlines, Methods and Applications of Analysis, 19 (2012) 211--242.
      7. G. Misiolek and T. Yoneda, Ill-posedness examples for the quasi-geostrophic and the Euler equations, in Analysis, Geometry and Quantum Field Theory, Contemporary Mathematics, Amer. Math. Soc., Providence, RI, (2012) 251--258.
      8. S. Ibrahim and T. Yoneda, Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data, J. Math. Anal. Appl., 396 (2012) 555--561.
      9. H. Koba, A. Mahalov and T. Yoneda, Global well-posedness for the rotating Navier-Stokes-Boussinesq equations with stratification effects, Adv. Math. Sci. Appl., 22 (2012) 61--90.
      10. E. Nakai and T. Yoneda, Bilinear estimates in dyadic BMO and the Navier-Stokes equations, J. Math. Soc. Japan, 64 (2012) 399--422.
      11. Y. Giga, A. Mahalov and T. Yoneda, On a bound for amplitudes of Navier-Stokes flow with almost periodic initial data, J. Math. Fluid Mech., 13 (2011) 459--467.
      12. E. Nakai and T. Yoneda, Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations, Hokkaido Math. J., 40 (2011) 67--88.
      13. P. Konieczny and T. Yoneda, On dispersive effect of the Coriolis force for the stationary Navier-Stokes equations, J. Diff. Eq., 250 (2011) 3859--3873.
      14. T. Yoneda, Long-time solvability of the Navier-Stokes equations in a rotating frame with spatially almost periodic large data, Arch. Ration. Mech. Anal., 200 (2011) 225--237.
      15. Y. Taniuchi, T. Tashiro and T. Yoneda, On the two-dimensional Euler equations with spatially almost periodic initial data, J. Math. Fluid Mech., 12 (2010) 594--612.
      16. T. Yoneda, Ill-posedness of the 3D-Navier-Stokes equations in a generalized Besov space near BMO^{-1}, J. Funct. Anal., 258 (2010) 3376--3387.
      17. E. Nakai and T. Yoneda, Construction of solutions for the initial value problem of a functional-differential equation of advanced type, Aeq. Math., 77 (2009) 259 -- 272.
      18. Y. Giga, H. Jo, A. Mahalov and T. Yoneda, On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data, Physica D, 237 (2008) 1422--1428.
      19. Y. Sawano and T. Yoneda, Quarkonial decomposition suitable for functional-differential equations of delay type, Math. Nachr., 281 (2008) 1810--1822.
      20. N. Kikuchi, E. Nakai, N. Tomita, K. Yabuta and T. Yoneda, Calderon-Zygmund operators on amalgam spaces and in the discrete case, J. Math. Anal. Appl., 335 (2007) 198--212.
      21. Y. Sawano and T. Yoneda, On the Young theorem for amalgams and Besov spaces, Int. J. Pure Appl. Math., 36 (2007) 197--205.
      22. T. Yoneda, On the functional-differential equation of advanced type f'(x)=af(λx), λ>1, with f(0)=0, J. Math. Anal. Appl., 332 (2007) 487--496.
      23. T. Yoneda, On the functional-differential equation of advanced type f'(x)=af(2x) with f(0)=0, J. Math. Anal. Appl., 317 (2006) 320--330.
      24. T. Yoneda, Spline functions and n-periodic points (Japanese), Trans. Japan Soc. Ind. Appl. Math., 15 (2005) 245--252.

      Honors and Awards

      1. The Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology:The Young Scientists’ Prize（科学技術分野の文部科学大臣表彰若手科学者賞） April 2014.
      2. MSJ Tatebe Katahiro Prize（日本数学会賞：建部賢弘特別賞）September 2012.
      3. Inoue Research Award for Young Scientists（井上研究奨励賞）February 2012.
      4. Postdoctoral Fellowship Award, Pacific Institute for the Mathematical Sciences September 2010-August 2012
      5. Postdoctoral Fellowship Award, Institute for Mathematics and its Applications September 2009-August 2011
      6. Chairman Award for Outstanding Ingenuity and Creativity（数理科学研究科長賞）, University of Tokyo, March 2009.
      7. JSPS Research Fellowship for Young Scientists（学振特別研究員DC1）: April 2006-March 2009,　at University of Tokyo.

      Grants

      1. 基盤研究(A)(代表)2024--2028「物理と数学の協働による乱流クロージャー問題解決に向けた機械学習理論の創出」
      2. 基盤研究(C)(分担)2021年度～2025年度 21K03304「平均振動量・増大度が一様でない関数空間の理論と応用」
      3. 基盤研究(B)(代表)2020--2023「物理と数学の協働によるNavier-Stokes乱流のエネルギーカスケードの解明」
      4. 基盤研究(B)(分担)2018--2021「粘弾性流体に特有な渦の数理解析」
      5. 基盤研究(B)(分担)2018--2021「曲面上の渦力学：曲面の幾何がもたらす新しい流体運動の数理科学」
      6. 基盤研究(B)(分担)2015--2019「実解析・調和解析に由来する関数空間の理論の深化と応用」
      7. 基盤研究(B)(分担)2017--2021「流体方程式における非共鳴波動相互作用」
      8. Grant-in-Aid for Young Scientists A, 17H04825（科研費、若手研究 A）　2017--2019 「数学的アプローチによる様々な流体物理現象の解明」
      9. 稲盛財団研究助成 2017年4月--2019年3月「ナヴィエ・ストークス方程式の爆発問題の解明に向けた渦の非線形相互作用に対する大規模数値計算」
      10. Grant-in-Aid for Young Scientists B（科研費、若手研究 B）　2013--2015 「流体方程式に対する実解析的手法および数値計算」
      11. 住友財団基礎科学研究助成　2013年11月--2014年11月「ナヴィエ・ストークス方程式の爆発問題の解明に向けた流体乱流の大規模数値計算」（共同研究者：斉木吉隆）
      12. 2013年度、北海道大学情報基盤センター共同研究実施に係る学際大規模計算機システム利用：斉木・米田グループとして400万秒分、スパコンのファイル容量が0.6TB分

      Selected invited talks

      1. April 2022--present

        1. TBA, Singularities in Fluids and General Relativity, Old and new challenges in fluid equations: regularity, singularity and stability, the Institute for Mathematical Sciences in Singapore, Dec 16--20, 2024.
        2. TBA, Patterns in solutions to the incompressible Euler equations, The Mathematical Research and Conference Center, Bedlewo (Poland), August 5--9, 2024.
        3. Recent development in the study of 3D Navier-Stokes turbulence in terms of scale local vortex stretching, workshop on Analysis of PDEs in Fluid, Osaka Metropolitan U., March 14--15, 2024.
        4. Fourier analytical understanding of chaos in RNN and non-separable function space in DNN, Prediction Science Seminar, RIKEN (online), Feb. 14, 2024.（予測科学セミナー，理化学研究所）
        5. Mathematical structure of perfect predictive reservoir computing for autoregressive type of time series data, workshop on Infinite dimensional Geometry and PDEs, BIRS research station, Banff, Canada, Nov. 5--10, 2023
        6. 自己回帰的で発散しない時系列データに対するリザバーコンピューティングの完全予測構造について 第１４回　微分方程式とデータサイエンス研究会, Kanazawa UNiv., Oct. 18, 2023.
        7. Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching and related topics, minisymposium ``Problems in incompressible fluid flows: Stability, Singularity, and Extreme Behavior", International Congress on Industrial and Applied Mathematics -- ICIAM 2023, Tokyo, Japan, Aug. 20--25, 2023
        8. Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching and related topics, RIMS workshop, Analysis of fluid dynamical PDEs, Kyoto Univ., March 13--15, 2023.
        9. Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching and related topics, International workshop on Ergodic theory, dynamical systems and climate sciences, Hokkaido Univ., Sapporo, Mar. 6--10, 2023.
        10. Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching and related topics, 2023 Winter Workshop on Mathematical Analysis of Fluids, Busan, Korea, Jan-Feb. 2023.
        11. Pointwise convergence theorem of mini-batch gradient descent in terms of deep neural network, Hokudai MMC Seminar, Hokkaido Univ., Jan. 6 2023. 深層ニューラルネットワークのミニバッチ勾配降下に対する各点収束定理，北大MMCセミナー
        12. Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching and related topics, 量子流体における数理構造の解明，大阪公立大学数学研究所，Jan. 23--25, 2023.
        13. Recent topics on well-posedness and stability of incompressible fluid and related topics, Summer Graduate School, Mathematical Sciences Research Institute (MSRI), Hilo, Hiwaii, USA, July 18, 2022 - July 29, 2022
        14. Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching, RIMS Workshop Mathematical Analysis in Fluid and Gas Dynamics, July 6--8, 2022
        15. Mathematical reformulation of the Kolmogorov-Richardson energy cascade and mathematical analysis of extreme dissipation in terms of vortex stretching, 第77回東工大数理解析セミナー, Tokyo inst. tech., April 22, 2022

      2. April 2016--March 2022

        1. 流れのあらわし方, 流体若手夏の学校2021(online), Aug. 28-29, 2021
        2. Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching, Sapporo symposium, Hokkaido Univ.(online), Aug. 2021
        3. Quasi-streamwise vortices and enhanced dissipation for the incompressible 3D Navier-Stokes equations, analysis and PDEs seminar, Cergy Paris Universite (online), France, Jan. 2021
        4. Vortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equations, International Workshop on Multi-Phase Flows: Analysis, Modelling and Numerics, Waseda University (online), Tokyo, Dec. 1--4 2020
        5. TBA, 流体若手夏の学校2020（来年度へ延期）
        6. Vortex stretching and a modified zeroth law for the incompressible 3D Navier-Stokes equations, Applied Math And Analysis Seminar, Duke University, USA, April 1, 2020 (cancelled due to the COVID-19 outbreak).
        7. Instantaneous vortex stretching and energy cascade on the incompressible 3D Euler equations, National Chiao Tung University, Hsinchu, Taiwan, Aug. 13.
        8. Recent topics on well-posedness and stability of incompressible fluid and related topics, Summer Graduate School, Mathematical Sciences Research Institute (MSRI), Berkeley, CA, USA, July 22, 2019 - Aug. 02, 2019 (lecture on 23 and 29-2)
        9. 瞬間的な渦伸長を生成する3次元Euler流・それに関連するzeroth lawについて:A remark on the zeroth law and instantaneous vortex stretching on the incompressible 3D Euler equations,京都大学応用数学セミナー:Kyoto University Applied Mathematics Seminar (KUAMS), Kyoto Unviersity, May 21 2019.
        10. Instantaneous vortex stretching and energy cascade on the incompressible 3D Euler equations, KIAS workshop, Mathematics of Fluid Motion II: Theory and Computation, KIAS, Korea, Dec. 26-28 (talked at 27), 2018.
        11. Instantaneous vortex-stretching and anomalous dissipation on the 3D Euler equations, The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taipei, Taiwan, July 5 - July 9 (talk at 7), 2018
        12. Instantaneous vortex-stretching and anomalous dissipation on the 3D Euler equations, 2018 International Conference on Mathematical Fluid Dynamics School of Mathematics and Information Science, Henan Polytechnic University, May 25-27 (talk at 27), 2018.
        13. 様々な流体物理現象の数学解析：回転流体中のvortex breakdownと2次元乱流に現れるvortex thinning, 熊本大学応用解析セミナー, Dec. 9, 2017.
        14. An instability mechanism in the vorticity on the axis for the axisymmetric Euler equations, Princeton Tokyo Mathematical Fluid Dynamics, Princeton University, Princeton, USA, Nov.7--Nov. 9, 2017.
        15. A remark on trajectory behavior along the axis for the axisymmetric Euler equations with large uniform rotation, 2017 Program on Analysis of PDE: 2D Hydrodynamics and related Issues, Fudan University, Shanghai, China, Oct.30--Nov. 3, 2017.
        16. Pulsatile flowの乱流遷移とVortex breakdownに関する純粋数学的洞察の試み, SummerSchool 数理物理, University of Tokyo, Aug. 25--27.
        17. A weak type of norm inflation for solutions of the incompressible 2D Euler equations near the critical Besov space B^2_{2,1}, Harmonic Analysis and its Applications in Tokyo 2017, Nihon University, August 2(Wed) -- 4(Fri), 2017.
        18. A weak type of norm inflation for solutions of the incompressible 2D Euler equations near the critical Besov space B^2_{2,1}, 5th East Asian Conference in Harmonic Analysis and its Applications, Zhejiang University of Science and Technology, Hangzhou (杭州), China, June 9--13, 2017
        19. An instantaneous blowup of the axisymmetric Euler flow in well-posed Holder spaces (ten min. talk), Oberwolfach Workshop (Geophysical Fluid Dynamics), Oberwolfach, Germany, May 2017.
        20. Mathematical analysis of pulsatile flow and vortex breakdown, interdisciplinary/international seminar on nonlinear sciences, University of Tokyo, Mar. 13,14,22, 2017 (talk at 14).
        21. Pulsatile flowの乱流遷移に関する純粋数学的洞察の試み, 非線形現象と高精度高品質数値解析, 富山大学, Feb. 13--15, 2017. (talk at 15)
        22. Mathematical considerations of laminar-turbulent transition and vortex thinning in 2D turbulence, Tokyo-Berkeley Mathematics Workshop:Partial Differential Equations and Mathematical Physics University of Tokyo, Jan. 9--13, 2017. (talk at 11--13)
        23. 軸対称オイラー方程式の一方向流に対する不安定性について, 日本流体力学会 年会2016, Nagoya Inst. Tech., Sep. 26, 2016.
        24. フルネ・セレの公式と動標構を用いた3次元軸対称オイラー流の洞察,談話会, Tokyo Inst. Tech., July 6, 2016.

      3. April 2014--March 2016

        1. A local analysis of incompressible Euler flow, Fifth China-Japan Workshop on Mathematical Topics from Fluid Mechanics, Wuhan, China, Nov. 17-- Nov. 21 2015.
        2. Loss of continuity of the solution map for the Euler equations using large Lagrangian deformation. 10th International ISAAC Congress in Macau, Harmonic Analysis and PDEs,University of Macau, Aug. 3--8 2015. (talk at 5)
        3. Loss of continuity of the solution map for the Euler equations using multi-scale vorticities, Summer School on multiscale and geometric analysis, Hokkido University, Hokkaido, July 27--July 30 2015.
        4. Loss of continuity of the solution map for the Euler equations using large Lagrangian deformation. RIMS研究集会「流体と気体の数学解析」, RIMS Workshop on Mathematical Analysis in Fluid and Gas Dynamics, Kyoto Univ., July 8--10 2015.
        5. Loss of continuity of the solution map for the Euler equations in \alpha-modulation spaces including B^1_{\infty, 1} and C^{1+s} (0＜s＜1), 第7回 名古屋微分方程式研究集会, Nagoya University, March 3--5 2015.
        6. Loss of continuity of the solution map for the Euler equations, PDE seminar, University of Minnesota, January 28 2015
        7. 2次元渦度方程式に対する数学解析：三波相互作用とLagrangian deformation, 山田道夫先生還暦記念研究集会「非線形現象の数理」, Wakayama, Dec. 26--28 2014.
        8. Topics in Mathematical fluid dynamics, CMMSC seminar in dynamical system and differential equations, National Chiao Tung University, Taiwan, Nov. 24 2014.
        9. Local ill-posedness of the Euler equations in a critical Besov Space, 九州関数方程式セミナー, Fukuoka Univ., Fukuoka, Nov. 7 2014.
        10. Local ill-posedness of the Euler equations in a critical Besov space , 調和解析駒場セミナー, Univ. of Tokyo, Tokyo, Oct. 25 2014.
        11. オイラー方程式の$C^1$クラスにおける局所非適切性について， 渦の特徴付け, Hokkaido Univ., Sapporo, July 28--30, 2014
        12. ミレニアム懸賞問題：Navier-Stokes方程式, 応用解析特別講義, Ibaraki Univ., Ibaraki, June 3 2014.
        13. 3次元Navier-Stokes流の局所的振る舞いに対する微分幾何学的アプローチ，談話会，Tokyo Inst. of Tech., Tokyo, May 28 2014.
        14. Navier-Stokes流の局所的振る舞いに対する特性曲線法の応用, 応用解析研究会, Waseda Univ., Tokyo, May 17, 2014

      Students and Postdoctoral assosiates (since April 2014)

      1. Master students
        1. 上野健太 (April 2015--Mar. 2017) 円環領域内の2次元非圧縮オイラー流における渦度勾配の時間発展について
        2. 中井 拳吾 (April 2015--Mar. 2017) Navier-Stokes方程式の解の爆発と渦度の方向ベクトルの関係性
        3. Hu Xin (April 2018--Mar. 2020) Fractional Hydrodynamic Limit for the Scaled Boltzmann Equation
        4. Bao Han（ホウカン） (April 2023--Mar. 2024) 株価時系列データにおける古典ARIMA モデルとリザ バーコンピューティングモデルの比較, A comparison between classical ARIMA model and reservoir computing model based on stock price time series data
        5. 新谷裕暉 (April 2023--present) 遅れ座標系とReal-time bandpass-filterを用いたリザバーコンピューティング
        6. JIN MINGXIN（キンメイキン） (April 2024--present)遅れ座標系とReal-time bandpass-filterを用いたリザバーコンピューティング
        7. LAN Tian（ランテン） (April 2024--present)遅れ座標系とReal-time bandpass-filterを用いたリザバーコンピューティング
        8. WAN LIPIN （マンリピン） (April 2024--present)遅れ座標系とReal-time bandpass-filterを用いたリザバーコンピューティング
      2. Doctor students
        1. Hu Xin (April 2020--Mar. 2024) On the hydrodynamic limit of the Boltzmann equation and its numerical computation
        2. 鶴橋　知典(April 2020--Mar. 2023) On microscopic interpretation for convex integration and self-similar structure of vortices in turbulence　
        3. 中井 拳吾 (April 2017--Mar. 2020) Machine-learning Construction of a Model and Refined Regularity Criterion on Fluid Equations
      3. Postdocs
        1. 伊藤　翼（Tsubasa Ito）(April 2014--March 2016)
        2. 許　本源（PenYuan Hsu）(Oct. 2014--Sep. 2015)
        3. 柏原崇人 (Takahito Kashiwabara) (April 2015--Sep. 2015)
        4. 田内大渡(Taito Tauchi)(April 2019--Mar. 2020)
        5. 清水雄貴(Yuuki Shimizu)学振PD (April 2021--Mar. 2024)
        6. 顧仲陽(Zhongyang Gu) (April 2022--Mar. 2023)
        7. Pritpal Matharu Mitacs-JSPS summer program (April 2022--June 2022)
        8. 神野拓哉(Takuya Jinno) RA (Nov. 2022--Mar. 2024)
        9. 川澄亮太(Ryota Kawasumi) (Jan. 2024--Mar. 2024)
        10. 渡邊大記(Daiki Watanabe) (April 2024--present)

        Organizer (since April 2016)

        1. Dynamics and Design Conference 2024（D&D2024）, 第67回理論応用力学講演会・乱流OS Sep.3-6, 2024
        2. ICIAM2023, Minisymposium, Recent development of mathematical geophysics, Waseda Univ., Tokyo, August 20-25, 2023
        3. Recent topics on well-posedness and stability of incompressible fluid and related topics, Summer Graduate School, Mathematical Sciences Research Institute (MSRI), Hilo, Hawaii, USA, July 18, 2022 - July 29, 2022
        4. Tokyo-NTU joint conference, UTokyo-NTU Joint Symposium in Mathematics (parallel session), University of Tokyo, (Dec.9-10 2019)
        5. RIMS合宿型セミナー（研究題目：物理と数学両アプローチによる地球流体力学の諸問題の追求）, Niseko, Hokkaido, Sep.6--10, 2019.
        6. Recent topics on well-posedness and stability of incompressible fluid and related topics, Summer Graduate School, Mathematical Sciences Research Institute (MSRI), Berkeley, CA, USA, July 22, 2019 - Aug. 02, 2019
        7. 2019年度日本応用数理学会年会 実行委員会(Sep. 3-5 2019)
        8. 日本応用数理学会学会誌の編集委員会委員(April 2017--Mar. 2020)
        9. 流体力学会年会における「流体数理」のセッションオーガナイザー(2016,2017,2018,2019,2020,2021)

        Working experience (since April 2014)

        1. 流体運動の数学研究とその社会的意義, 公開講座, 『数理科学の広がり』 東京大学, Nov. 23, 2019.
        2. 高校生と大学生のための金曜特別講座， 無限にまつわる厄介な数学問題・それを巧妙に避けるルベーグ積分， 東京大学，Dec. 7, 2018
        3. オーガナイザー，中学生のための玉原数学教室（第12回,第13回）， 玉原国際セミナーハウス， Oct. 13, 2018, Octo 19 2019.
        4. JST数学キャラバン:流体の数学研究とその社会的意義について，茨城県立水戸第二高校，水戸，Jan. 27, 2018
        5. 一般向けの講演：流体の数学研究とその社会的意義について, 東工大オープンキャンパス，Tokyo Inst. Tech. Aug. 8, 2014
        6. 一般向けの講演：流体の数学研究とその社会的意義について, ホームカミングデイ, Tokyo Inst. Tech. May 25, 2014

        Editorial services

        1. 2014 April--2016 March, Editorial board: Kodai Mathematical Journal

        大学院生に対するメッセージ

        私の大学院ゼミでは、時系列データに対する機械学習（リザバーコンピューティング）や、ARモデル等の従来モデルの改善がテーマの一つになります。 フーリエ解析学を基にして機械学習（特にRNN）を再洞察している点がこの研究室の特徴であり、特に、誰でも扱えるRNNの構築を目指しています。
        ゼミではPythonを使います。

        機械学習の基礎（画像認識とリザバーコンピューティング）を講義するので、その履修を必須とします。

        私自身は、フーリエ解析的手法に基づく流体方程式の数学解析・乱流物理の研究を進めています。しかし 「乱流などの非線形構造に対する数理的理解を深めるためには、機械学習の数理構造の理解が有効だろう」という見解に至り、このように機械学習の研究も進めています。

        遠い将来を見据えた数学研究のスケッチ（スケール間相互作用理解と機械学習理解の等価性）

        深層学習から導かれる普遍構造と、物理法則から導かれる物理構造の根本的違いこそ、遠い将来を見据えた長期的研究テーマとなる。 その理解のために、まずは物理で基本となる「次元解析」を説明しよう。次元解析とは、物理法則がスケール変換に対して本質的に変わらないことを意味する。 例えば、雲の振る舞い自体は、近く（例えば１０m先）で観測しても遠く（例えば1km先）で観測ても実はあまり変化しない（時間スケールは変化する）。そして、雲は、小さな渦と大きな渦の振る舞いが互いに影響し合っている（スケール間相互作用）。要は、半径10mの雲の渦と半径1ｋｍ の雲の渦の物理構造は本質的には同じである（数学の偏微分方程式論においても、スケール変換不変性が重要な役割を担っている）。

        という枠組みの中で物理構造は考えられている。

        しかしながら、力学系のリアプノフ指数を勘案すると、スケールが小さくなればなるほど初期値に対する鋭敏性が大きくなってしまう。要は、そういった小スケールの挙動を本気で調べようとすればするほど、未来予測のための物理モデル構築が本質的に困難になってしまう。よって、「次元解析」を超えるパラダイムシフトが必要であろう。

        すなわち、単独スケールへ射影された非線形物理現象のモデル構築には、そういったスケール間相互作用が（暗黙の内に）うまく組み込まれているモデルであり、そして、そこに内包される物理構造は「各スケール運動の相互作用」という枠組みを超えているモデルである。

        要は、一旦他スケールへ出て行ってしまった物理作用の一部がそのターゲットとなるスケールへと戻ってきている筈である。すなわち、そのスケール間を往復している物理作用が、単独スケール内において何かしらの「数式」として表現できることだろう、そして、そこに機械学習が登場する（乱流クロージャー問題に対する有望な解決策）。 要は「機械学習の数理構造の理解とそういったクロージャ―問題理解は等価であろう」という（私自身の）見立てである。