Hiroyuki Chihara

updated on 21 August 2026

Sugar Loaf from Botafogo beach, Rio de Janeiro on 30 July 2025

Hiroyuki Chihara College of Education University of the Ryukyus Nishihara, Okinawa 903-0213, Japan		2 June 2025 NUS IMS Singapore		19 June 2026 Academia Sinica Taipei, Taiwan

I am a mathematician living in Okinawa Island, Japan. Since 2020, I have been working on the microlocal analysis of integral geometry. My main research objects are integral transforms such as geodesic X-ray transforms on Riemannian manifolds and double fibration transforms on product manifolds. The simplest example of these transforms is the classical X-ray transform on the Euclidean space, whose foundational mathematical principles underpin CT scanners and medical imaging.

Since 2021, as part of my professional upskilling, I have been modernizing and visualizing his university lectures on elementary number theory, calculus, and linear algebra using the Julia programming language and its interactive notebook environment, Pluto.jl. In 2025, upon a strong suggestion from ChatGPT to present a demonstration of his dynamic course materials at ATCM 2025 (The 30th Asian Technology Conference in Mathematics), I expanded his academic scope to include mathematics education and computational thinking.

I generally rely solely on non-Japanese media, and I truly envy the grounded nations of Asia and Oceania; I would love to work in a country like that someday.

Membership
- AMS CHHRXI
- SIAM 020880668
- KAKEN 70273068
Current and upcoming projects
- Geodesic X-ray transforms on Finsler manifolds and ocean acoustic tomography
- Pseudodifferential calculus on singular manifolds and applications
- Double fibration transforms and limited data tomograpy
- Learning English, Julia Programming Language and applied harmonic analysis
Recent Talks
- 31 October - 2 November 2026, Normal operators of double fibration transforms, Sino-Franco-Japanese Joint Workshop - Spectral Methods in Partial Differential Equations, Nanjing University of Aeronautics and Astronautics.
- 15 - 19 June 2026, Normal operators of double fibration transforms, Session: Inverse Problem and Applications, 10th Pacific Rim Conference on Mathematics, Academia Sinica, Taiwan, slides.
- 14 - 16 January 2026, Normal operators of double fibration transforms, Inverse problems for partial differential equations and related areas, RIMS, Kyoto University, Kyoto, abstract, slides, Pluto html.
- 13 - 16 December 2025, Computational explorations in modern number theory: the Green–Tao theorem and the abc conjecture ATCM 2025, The 30th Asian Technology Conference in Mathematics, Ateneo de Manila University, Manila, html, handout, GitHub, Google Colab.
- 28 July - 1 August 2025, Double fibration transforms with conjugate points, MS-04 Integral geometry, rigidity and geometric inverse problems, AIP 2025, 12th Applied Inverse Problems Conference, FGV EMAp, Rio de Janeiro, abstract, slides.
- 9 - 13 December 2024, Geodesic X-ray transform and streaking artifacts on simple surfaces or on spaces of constant curvature, Session: Microlocal Analysis and Inverse Prolems, Joint meeting of the NZMS, AustMS and AMS, Sir Owen G Glenn Building, University of Auckland, slides.
Mathematics Papers and Preprints
1. The symbol of the normal operator for the d-plane transform on the Euclidean space, submitted, arXiv:2412.18197, 5 pages.
2. Geodesic X-ray transform and streaking artifacts on simple surfaces or on spaces of constant curvature, Vietnam Journal of Mathematics, published online, doi.
3. Joint work with Shubhan R. Jathar and Jesse Railo, The matrix weighted real-analytic double fibration transforms, Annales Fennici Mathematici, 51(1) (2026), pp.353-376, doi.
4. Microlocal analysis of double fibration transforms with conjugate points, J. Geom. Anal., 36 (2026), ID 68, 22 pages, doi.
5. Microlocal analysis of d-plane transform on the Euclidean space, SIAM J. Math. Anal., 54(6) (2022), pp.6254-6287, doi.
6. Bargmann transform on the space of hyperplanes, J. Fourier Anal. Appl., 28 (2022), article No.72, 21 pages, doi.
7. Inversion of higher dimensional Radon transforms of seismic-type, Vietnam Journal of Mathematics, 49 (2021), pp.1185-1198, doi.
8. Inversion of seismic-type Radon transforms on the plane, Integral Transforms Spec. Funct., 31 (2020), pp.998-1009, doi.
9. Bargmann-type transforms and modified harmonic oscillators, Bull. Malays. Math. Sci. Soc., 43 (2020), pp.1719-1740, doi.
10. Holomorphic Hermite functions in Segal-Bargmann spaces, Complex Anal. Oper. Theory, 13 (2019), pp.351-374, doi.
11. Joint work with Takashi Furuya and Takumi Koshikawa, Hermite expansions of some tempered distributions, J. Pseudo-Differ. Oper. Appl., 9 (2018), pp.105-124, doi.
12. Holomorphic Hermite functions and ellipses, Integral Transforms Spec. Funct. 28 (2017), pp.605-615, doi.
13. Fourth-order dispersive systems on the one-dimensional torus, J. Pseudo-Differ. Oper. Appl., 6 (2015), pp.237-263, doi.
14. Joint work with Eiji Onodera, A fourth-order dispersive flow into Kähler manifolds, Z. Anal. Anwend., 34 (2015), pp.221-249, doi.
15. Schrödinger flow into almost Hermitian manifolds, Bull. Lond. Math. Soc., 45 (2013), pp.37-51, doi.
16. Joint work with Eiji Onodera, A third order dispersive flow for closed curves into almost Hermitian manifolds, J. Funct. Anal., 257 (2009), pp.388-404, doi.
17. Bounded Berezin-Toeplitz operators on the Segal-Bargmann space, Integral Equations Operator Theory, 63 (2009), pp.321-335, doi.
18. Gain of analyticity for semilinear Schrödinger equations, J. Differential Equations, 246 (2009), pp.681-723, doi.
19. Resolvent estimates related with a class of dispersive equations, J. Fourier Anal. Appl., 14 (2008), pp.301-325, doi.
20. The initial value problem for a third order dispersive equation on the two dimensional torus, Proc. Amer. Math. Soc., 133 (2005), pp.2083-2090, doi.
21. The initial value problem for Schrödinger equations on the torus, Int. Math. Res. Not., 2002:15 (2002), pp.789-820, doi.
22. Smoothing effects of dispersive pseudodifferential equations, Comm. Partial Differential Equations, 27 (2002), pp.1953-2005, doi.
23. Gain of regularity for semilinear Schrödinger equations, Math. Ann., 315 (1999), pp.529-567, doi.
24. The initial value problem for the elliptic-hyperbolic Davey-Stewartson equation, J. Math. Kyoto Univ., 39 (1999), pp.41-66, doi.
25. The initial value problem for cubic semilinear Schrödinger equations, Publ. Res. Inst. Math. Sci., 32 (1996), pp.445-471, doi.
26. Global existence of small solutions to semilinear Schrödinger equations, Comm. Partial Differential Equations, 21 (1996), pp.63-78, doi.
27. Global existence of small solutions to semilinear Schrödinger equations with gauge invariance, Publ. Res. Inst. Math. Sci., 31 (1995), pp.731-753, doi.
28. Local existence for semilinear Schrödinger equations, Math. Japon., 42 (1995), pp.35-52, url.
29. Local existence for the semilinear Schrödinger equations in one space dimension, J. Math. Kyoto Univ., 34 (1994), pp.353-367, doi.
Refereed Conference Papers
1. Smoothing effects of dispersive pseudodifferential equations, Report, Mathematisches Forschungsinstitut Oberwolfach, 20 (2002), pp.2-3.
2. The initial value problem for semilinear Schrödinger equations, GAKUTO Internat. Ser. Math. Sci. Appl., 10 (1997), pp.19-24.
Names of TeX files of recent papers
- used: char kway teow, new series siglap, esplanade.
- unused: bayshore, tampines, orchard, bishan, chinatown, bugis, eunos, clementi, harbourfront, ...
Mathematics Education and Others
1. Paper: Mathematics Education, submitted.
2. Paper: Educational Practice Report, submitted.
3. Working Paper: Explicit formulas for the Jordan normal forms and matrix exponentials of 2×2 matrices, Zenodo, doi.
4. Working Paper: Seismic intensity and typhoon categories: the need for quantitative clarity in Japanese disaster communication, Zenodo, doi.
5. Hands-On Workshop: schedule undecided, Julia and Python on Google Colab, handout, GitHub, Google Colab.
6. Contributed Talk: 13 - 16 December 2025, Computational explorations in modern number theory: the Green–Tao theorem and the abc conjecture, ATCM 2025, The 30th Asian Technology Conference in Mathematics, Ateneo de Manila University, Manila, html, handout, GitHub, Google Colab.

Upcoming Events
- 31 August - 4 September 2026, Workshop on Mathematical Approaches to Modern AI Challenges, Mathematical Foundations & Methodologies for Artificial Intelligence and Data-Driven Scientific Computing, IMS, National University of Singapore.
- 31 October - 2 November 2026, Sino-Franco-Japanese Joint Workshop - Spectral Methods in Partial Differential Equations, Nanjing University of Aeronautics and Astronautics.
- AIP 2027 (13th Applied Inverse Problems Conference), TBA.
- November 2027, AIFE 2027 (AI for Education Conference 2027). National Institute of Education, Nanyang Technological University, AIFE 2026, AIFE 2025, AIFE 2024.
- December 2027, ATCM 2027 (The 32nd Asian Technology Conference in Mathematics).
- 14 August - 15 December 2028, Inverse Problems and Applications, SLMath.
Mathematical Institutes is Asia-Pacific
- Institute of Mathematics, Academmia Sinica.
- Mathematics Division, NCTS (National Center for Theoretical Sciences).
- Department of Mathematics, National Taiwan University.
- The Institute for Mathematical Sciences (IMS), National University of Singapore.
- Department of Mathematics, National University of Singapore.
- Department of Mathematics, Nanyang Technological University.
- Yau Mathematical Science Center, Tsinghua University.
- Hong Kong Institute for Advanced Study (HKIAS), City University of Hong Kong.
- The Liu Bie Ju Centre for Mathematical Sciences (LBJ Centre), City University of Hong Kong.
- Department of Mathematics, City University of Hong Kong.
- Department of Mathematics, Hong Kong University of Science and Technology.
- Department of Mathematics, Chinese University of Hong Kong.
- Department of Mathematics, University of Hong Kong.
- Vietnam Institute for Advanced Study in Mathematics.
- Institute of Mathematics, Vietnam Academy of Science and Technology.
- Sydney Mathematical Research Institute, University of Sydney.
Webinars
- University of Oxford, Learning on Graphs and Geometry - LoG².
- USACM, The Mathematical Methods in Computational Engineering & Sciences TTA.
Mathematics Journals in Asia-Pacific
Past Events managed in this site
- 29 November - 1 December 2023, Spectral and Scattering Theory and Related Topics 2023, RIMS, Kyoto U.
- TSUBO (Naha Workshop on Mathematical Analysis)
- MIMIBUKURO (Ear Bag of Mathematical Analysis)
- Tsukuba RCMS Symposium on Mathematical Analysis

English pronunciation of linux
Update of Julia Programming Language for linux
- Installatin
  rm .juliaup
  curl -fsSL https://install.julialang.org | sh
- Jupyter notebook
  add IJulia
  build IJulia
- Remove old versions in Jupyter notebook
  jupyter kernelspec list
  jupyter kernelspec uninstall KERNEL_NAME
DX/AX and Digital Accessibility
- Enhancing Digital Accessibility of Mathematics, 15 April 2026, American Mathematical Society.
- Markdown Guide
- Ghostwriter (markdown editor)
- Pandoc a universal document
- Quarto
- pandoc: creating a PDF containing Japanese
  pandoc FILENAME.md -o FILENAME.pdf --pdf-engine=xelatex -V documentclass=bxjsarticle -V classoption=pandoc
Electronic Travel Authority
English pages and articles
- MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning (2018), YouTube
- MIT Introduction to Computational Thinking, 18.S191 (Fall 2020), YouTube
- MIT 6.S191 Introduction to Deep Learning, YouTube
- MIT 18.337J/6.338J Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications, YouTube
- Modernizing Curriculum: A Machine Learning Plan with Rebecca Willett, 7 April 2026, American Mathematical Society.
- Manuchehr Aminian, The connection between applied mathematics and deep learning SIAM NEWS, 1 October 2020.
- Davide Castelvecchi, Long-awaited mathematics proof could help scan Earth's innards, Nature 542, (2017), pp.281–-282, 16 February 2017, doi: 10.1038/nature.2017.21439 .
Lifelong Learning
- SkillsFuture, The Government of Singapore, url.
- How can SkillsFuture help me?, 28 Novemver 2024, Ministry of Education, Singapore, url.
- SkillsFuture for Educators (SFEd), 4 March 2020, Academy of Singapore Teachers, url.
- Janice Loo, Teach Less, Learn More, 19 March 2018, National Library Board Singapore, url.
- Learn for Life: Confidence for a New Tomorrow, 8 March 2022, Ministry of Education, Singapore, url.
- Smart Nation Singapore url.
Mathematics Education
- AME (Association of Mathematics Educators), Singapore.
- Mathematics & Mathematics Education Department, National Institute of Education, Singapore.
- Department of Mathematics and Information Technology, Faculty of Liberal Arts and Social Sciences, The Education University of Hong Kong.
- ICME (International Congress on Mathematical Education).
- ACTM (The Asian Technology Conference in Mathematics).
- APSCE (The Asia-Pacific Society for Computers in Education).
- Ban Heng Choy, Teacher education in Singapore: An insider view, Journal für LehrerInnenbildung, 23(4) (2023), pp.66-77, Springer, Cham, 2015, doi.
- Keng Cheng Ang and Marc Yi Fei Yeo, Mathematics teachers’ perceptions and practice of computational thinking, The Electronic Proceedings of the 30th ATCM (The 30th Asian Technology Conference in Mathematics), pdf.
- Chong Ket Fah, Weng Kin Ho, Hon Wai Leong, and Eng Guan, From primary school to university in Singapore: Recent initiatives in the teaching of digital literacy and computational thinking, ICME-15 (2024), TSG 1.9: Teaching and learning of computational thinking, pdf.
- Tin Lam Toh, A glimpse into the mathematics education research in Singapore, Hiroshima Journal of Mathematics Education, 13 (2020), pp.99-120, doi.