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D-Index & Metrics

Mathematics

D-Index
42
Citations
7010
World Ranking
1797
National Ranking
769

J. William Helton 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 J. William Helton 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: 82 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: 260 publications — 79th percentile

79% of scientists in this discipline score the same or lower.

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

J. William Helton 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 J. William Helton 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: 137 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: 42 D-Index — 51st percentile

51% of scientists in this discipline score the same or lower.

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

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society

Overview

J. William Helton is affiliated with the University of California, San Diego in the United States. Their research spans multiple fields, with significant contributions in computer science and mathematics.

The primary areas of study for Helton include computational theory and mathematics, artificial intelligence, algebra and number theory, mathematical physics, and applied mathematics. Their work covers a range of topics such as quantum computing algorithms and architecture, advanced topics in algebra, matrix theory and algorithms, computability and logic related to AI algorithms, polynomial and algebraic computation, advanced operator algebra research, and quantum information and cryptography.

Helton has published extensively, with papers appearing in several notable venues. Frequent publication outlets include arXiv (Cornell University), Annales Henri Poincaré, Journal of Functional Analysis, International Mathematics Research Notices, and Quantum.

Notable papers by Helton include:

  • Bianalytic free maps between spectrahedra and spectraballs, 2020, Journal of Functional Analysis
  • Synchronous Values of Games, 2024, Annales Henri Poincaré
  • Factorization of Noncommutative Polynomials and Nullstellensätze for the Free Algebra, 2020, International Mathematics Research Notices

Helton has collaborated with several researchers over their career. Frequent coauthors include Igor Klep, Adam Bene Watts, Aidan Epperly, Eric Evert, and Jurij Volčič.

Their work also intersects with the contributions of Adam Bene Watts, who has coauthored papers such as "Noncommutative Nullstellensätze and Perfect Games" (2023, Annales Henri Poincaré) and "Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators" (2024, Quantum), which are related by research themes.

Helton was recognized as a Fellow of the American Mathematical Society in 2013.

Best Publications

  • Linear matrix inequality representation of sets

    J. William Helton;Victor Vinnikov

  • H ∞ -optimal feedback controllers for linear multivariable systems

    B. Francis;J. Helton;G. Zames

  • Extending H-infinity Control to Nonlinear Systems: Control of Nonlinear Systems to Achieve Performance Objectives

    J. William Helton;Matthew R. James

  • “Positive” noncommutative polynomials are sums of squares

    J. William Helton

  • Semidefinite representation of convex sets

    J. William Helton;Jiawang Nie

  • NONCOMMUTATIVE CONVEXITY ARISES FROM LINEAR MATRIX INEQUALITIES.

    J. William Helton;Scott A. McCullough;Victor Vinnikov

  • Discrete time systems, operator models, and scattering theory

    J.William Helton

  • Every convex free basic semi-algebraic set has an LMI representation

    J. William Helton;Scott McCullough

  • Classical control using H∞ methods: theory, optimization, and design

    J. William Helton;Orlando Merino

  • Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions

    Joseph A. Ball;J. William Helton

  • Traces of commutators of integral operators

    J. William Helton;Roger E. Howe

  • Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets

    J. William Helton;Jiawang Nie

  • The matricial relaxation of a linear matrix inequality

    J. William Helton;Igor Klep;Igor Klep;Scott A. McCullough

  • Non-Euclidean functional analysis and electronics

    J. William Helton

  • Operator-valued Semicircular Elements: Solving A Quadratic Matrix Equation with Positivity Constraints

    J. William Helton;Reza Rashidi Far;Roland Speicher

  • Systems with infinite-dimensional state space: The Hilbert space approach

    Unknown

  • Worst case analysis in the frequency domain: The H ∞ approach to control

    Unknown

  • Proper analytic free maps

    J. William Helton;Igor Klep;Igor Klep;Scott McCullough

  • Integral operators: Traces, index, and homology

    J. William Helton;Roger E. Howe

  • Applications of realizations (aka linearizations) to free probability

    J. William Helton;Tobias Mai;Roland Speicher

  • POSITIVE POLYNOMIALS IN SCALAR AND MATRIX VARIABLES, THE SPECTRAL THEOREM AND OPTIMIZATION

    J. William Helton;Mihai Putinar;Tibi Constantinescu

  • The convex Positivstellensatz in a free algebra

    J. William Helton;Igor Klep;Scott McCullough

  • An introduction to design

    J. William Helton;Orlando Merino

Frequent Co-Authors

Joseph A. Ball
Joseph A. Ball Virginia Tech
Mihai Putinar
Mihai Putinar University of California, Santa Barbara
Roland Speicher
Roland Speicher Saarland University
Matthew R. James
Matthew R. James Australian National University
Roger Howe
Roger Howe Texas A&M University
Ciprian Foias
Ciprian Foias Texas A&M University
Allen Tannenbaum
Allen Tannenbaum Stony Brook University
Robert E. Skelton
Robert E. Skelton Texas A&M University
Pramod P. Khargonekar
Pramod P. Khargonekar University of California, Irvine
Bruce A. Francis
Bruce A. Francis University of Toronto

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