World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
41
Citations
7812
World Ranking
1894
National Ranking
27

Fumio Hiai publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Fumio Hiai sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 176 publications — 52nd percentile

52% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Fumio Hiai D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Fumio Hiai sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 41 D-Index — 49th percentile

49% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Overview

Fumio Hiai is affiliated with Tohoku University in Japan and conducts research primarily in the fields of Mathematics and Computer Science. Their scholarly work spans several subfields including Applied Mathematics, Mathematical Physics, Computational Theory and Mathematics, Artificial Intelligence, and Geometry and Topology.

Their main research topics cover a range of advanced mathematical and physical theories such as Mathematical Inequalities and Applications, Advanced Operator Algebra Research, Advanced Banach Space Theory, Matrix Theory and Algorithms, Spectral Theory in Mathematical Physics, Quantum Information and Cryptography, and Quantum Mechanics and Applications.

Fumio Hiai has contributed to several academic papers in notable journals and conferences. Recent publications include:

  • "Test-Measured Rényi Divergences," 2022, IEEE Transactions on Information Theory
  • "Nonhomogeneous Karcher equations with vector fields on positive definite matrices," 2021, European Journal of Mathematics
  • "Pusz-Woronowicz Functional Calculus and Extended Operator Convex Perspectives," 2021, Integral Equations and Operator Theory
  • "Some Continuity Properties of Quantum Rényi Divergences," 2023, IEEE Transactions on Information Theory
  • "Operator means deformed by a fixed point method," 2020, Advances in Operator Theory

Frequent collaborators of Hiai include researchers such as Milán Mosonyi, Yongdo Lim, Shuhei Wada, Hideki Kosaki, and Anna Jenčová, reflecting a focus on interdisciplinary and international cooperation.

The venues that frequently publish Hiai's work feature both preprint and peer-reviewed sources, with multiple contributions to arXiv (Cornell University), IEEE Transactions on Information Theory, European Journal of Mathematics, Integral Equations and Operator Theory, and Advances in Operator Theory.

In addition to journal articles, their contributions extend to book publications, including titles such as:

  • "Lectures on Selected Topics in von Neumann Algebras," 2021, published by EMS series of lectures in mathematics
  • "Quantum f-Divergences in von Neumann Algebras," 2021, published by Springer Science+Business Media

These books further emphasize their specialization in operator algebras and quantum information theory, fields that intersect abstract mathematics and theoretical physics.

Best Publications

  • Integrals, Conditional Expectations and Martingales of Multivalued Functions

    Fumio Hiai;Hisaharu Umegaki

  • The semicircle law, free random variables, and entropy

    Fumio Hiai;Dénes Petz

  • The Proper Formula for Relative Entropy and its Asymptotics in Quantum Probability

    Fumio Hiai;Dénes Petz

  • Log majorization and complementary Golden-Thompson type inequalities

    Tsuyoshi Ando;Fumio Hiai

  • Introduction to Matrix Analysis and Applications

    Fumio Hiai;Petz Denes

  • The Semicircle Law, Free Random Variables and Entropy (Mathematical Surveys & Monographs)

    Fumio Hiai;Denes Petz

  • QUANTUM f-DIVERGENCES AND ERROR CORRECTION

    Fumio Hiai;Milán Mosonyi;Milán Mosonyi;Dénes Petz;Cédric Bény

  • Matrix Analysis : Matrix Monotone Functions, Matrix Means, and Majorization

    Fumio Hiai

  • On the Quantum Rényi Relative Entropies and Related Capacity Formulas

    M Mosonyi;F Hiai

  • Different quantum f-divergences and the reversibility of quantum operations

    Fumio Hiai;Milán Mosonyi

  • The Golden-Thompson trace inequality is complemented

    Fumio Hiai;Dénes Petz

  • Sufficiency, KMS condition and relative entropy in von Neumann algebras.

    Fumio Hiai;Masanori Ohya;Makoto Tsukada

  • Minimizing indices of conditional expectations onto a subfactor

    Fumio Hiai

  • Convergence of conditional expectations and strong laws of large numbers for multivalued random variables

    Fumio Hiai

  • Means of Hilbert Space Operators

    Fumio Hiai;Hideki Kosaki

  • Means for Matrices and Comparison of their Norms

    Fumio Hiai;Hideki Kosaki

  • Operator log-convex functions and operator means

    Tsuyoshi Ando;Fumio Hiai

  • Log-majorizations and norm inequalities for exponential operators

    Fumio Hiai

  • Riemannian metrics on positive definite matrices related to means

    Fumio Hiai;Dénes Petz

  • Asymptotic Freeness Almost Everywhere for Random Matrices

    Fumio Hiai

Frequent Co-Authors

Dénes Petz
Dénes Petz Budapest University of Technology and Economics
Koenraad M. R. Audenaert
Koenraad M. R. Audenaert Royal Holloway University of London
Masanori Ohya
Masanori Ohya Tokyo University of Science
Marco Tomamichel
Marco Tomamichel National University of Singapore
Masahito Hayashi
Masahito Hayashi Chinese University of Hong Kong, Shenzhen
Mark Fannes
Mark Fannes KU Leuven

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