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J. William Helton

D-Index & Metrics

Discipline name D-Index World Ranking Current World Ranking National Ranking Current National Ranking Publications Citations
Mathematics 42 1797 1563 770 625 260 7010

J. William Helton publications per year

The chart shows the history of publications by J. William Helton between 1950 and 2025, highlighting the no. of papers published in each year and offering an overview of the publication velocity of this scholar. J. William Helton published across 76 years, from 1950 to 2025, averaging 3.9 papers a year. Output peaked at 30 publications in 1998. 5 of the 293 publications appeared in the last two years.

No. of publications
10 20 30
Bar chart. Horizontal axis: year, 1950 to 2025. Vertical axis: number of publications, 0 to 30. Peak 30 publications in 1998. 1950: 1 publication 1951: 0 publications 1952: 0 publications 1953: 0 publications 1954: 0 publications 1955: 0 publications 1956: 0 publications 1957: 0 publications 1958: 0 publications 1959: 0 publications 1960: 0 publications 1961: 0 publications 1962: 0 publications 1963: 0 publications 1964: 0 publications 1965: 0 publications 1966: 0 publications 1967: 0 publications 1968: 0 publications 1969: 0 publications 1970: 1 publication 1971: 0 publications 1972: 4 publications 1973: 2 publications 1974: 2 publications 1975: 2 publications 1976: 5 publications 1977: 0 publications 1978: 0 publications 1979: 0 publications 1980: 2 publications 1981: 1 publication 1982: 5 publications 1983: 3 publications 1984: 5 publications 1985: 5 publications 1986: 7 publications 1987: 14 publications 1988: 8 publications 1989: 7 publications 1990: 6 publications 1991: 5 publications 1992: 6 publications 1993: 6 publications 1994: 11 publications 1995: 7 publications 1996: 7 publications 1997: 6 publications 1998: 30 publications 1999: 18 publications 2000: 4 publications 2001: 3 publications 2002: 2 publications 2003: 6 publications 2004: 4 publications 2005: 4 publications 2006: 6 publications 2007: 5 publications 2008: 6 publications 2009: 10 publications 2010: 9 publications 2011: 6 publications 2012: 10 publications 2013: 5 publications 2014: 3 publications 2015: 2 publications 2016: 1 publication 2017: 2 publications 2018: 4 publications 2019: 6 publications 2020: 4 publications 2021: 6 publications 2022: 2 publications 2023: 2 publications 2024: 2 publications 2025: 3 publications
1950 2025

293 publications in total across all disciplines

View publications per year as a table
J. William Helton: publications per year, 1950 to 2025
Year Publications
1950 1
1951 0
1952 0
1953 0
1954 0
1955 0
1956 0
1957 0
1958 0
1959 0
1960 0
1961 0
1962 0
1963 0
1964 0
1965 0
1966 0
1967 0
1968 0
1969 0
1970 1
1971 0
1972 4
1973 2
1974 2
1975 2
1976 5
1977 0
1978 0
1979 0
1980 2
1981 1
1982 5
1983 3
1984 5
1985 5
1986 7
1987 14
1988 8
1989 7
1990 6
1991 5
1992 6
1993 6
1994 11
1995 7
1996 7
1997 6
1998 30
1999 18
2000 4
2001 3
2002 2
2003 6
2004 4
2005 4
2006 6
2007 5
2008 6
2009 10
2010 9
2011 6
2012 10
2013 5
2014 3
2015 2
2016 1
2017 2
2018 4
2019 6
2020 4
2021 6
2022 2
2023 2
2024 2
2025 3
Total 293
Download as CSV

J. William Helton publications per year - data summary

  • J. William Helton, a Mathematics scholar from University of California, San Diego, has 293 publications recorded across 76 years, from 1950 to 2025.
  • The oldest publication on record dates to 1950 and the most recent to 2025.
  • The most productive year is 1998, with 30 publications.
  • The least productive years with any output are 1950, 1970, 1981 and 2016, with 1 publication each.
  • 23 of the 76 years in the span carry no publications at all (1951, 1952, 1953, 1954 and others).
  • The rate of publication averages 3.9 papers per year over the whole span, or 5.5 per year counting only the 53 years with at least one publication.
  • The last 5 years on the chart (2021-2025) hold 15 publications, 5% of the career total.
  • Split into equal eras - 1950-1975: 12 publications (0.5 per year); 1976-2001: 171 publications (6.6 per year); 2002-2025: 110 publications (4.6 per year).
  • Comparing the opening and closing eras, the overall trend of publication is rising.

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.

No. of scientists
25 50 75 100
Bar chart with 100 bars. Horizontal axis: publications, 42–46 to 537+. Vertical axis: number of scientists, 0 to 112. Most scientists, 112, have 142–146 publications. The last bar groups every scientist with 537 publications or more. The highlighted bar, 257–261 publications, is where this scientist sits. 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 scientist 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientist 522–526 publications: 3 scientists 527–531 publications: 1 scientist 532–536 publications: 4 scientists 537+ publications: 100 scientists
42–46 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.

View publications distribution as a table
Number of Mathematics scientists by publication count, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
Publications Scientists This scientist
42–46 3
47–51 5
52–56 7
57–61 20
62–66 14
67–71 25
72–76 19
77–81 35
82–86 50
87–91 60
92–96 86
97–101 84
102–106 83
107–111 90
112–116 99
117–121 90
122–126 91
127–131 109
132–136 110
137–141 98
142–146 112
147–151 102
152–156 88
157–161 106
162–166 83
167–171 102
172–176 77
177–181 81
182–186 78
187–191 71
192–196 92
197–201 64
202–206 69
207–211 64
212–216 62
217–221 58
222–226 53
227–231 50
232–236 46
237–241 46
242–246 46
247–251 43
252–256 29
257–261 45 260
262–266 30
267–271 33
272–276 34
277–281 30
282–286 31
287–291 21
292–296 34
297–301 26
302–306 10
307–311 17
312–316 23
317–321 13
322–326 16
327–331 26
332–336 13
337–341 13
342–346 16
347–351 17
352–356 12
357–361 18
362–366 18
367–371 9
372–376 11
377–381 8
382–386 8
387–391 9
392–396 9
397–401 8
402–406 11
407–411 6
412–416 6
417–421 9
422–426 8
427–431 5
432–436 8
437–441 8
442–446 4
447–451 4
452–456 4
457–461 2
462–466 2
467–471 4
472–476 3
477–481 3
482–486 6
487–491 3
492–496 5
497–501 5
502–506 1
507–511 6
512–516 4
517–521 1
522–526 3
527–531 1
532–536 4
537+ 100
Download as CSV

J. William Helton publication distribution in Mathematics in 2026 - data summary

  • The chart plots the publication count of all 3,584 Mathematics scientists ranked by Research.com in 2026, grouped into 100 ranges running from 42–46 to 537+ publications.
  • J. William Helton, a Mathematics scholar from University of California, San Diego, records 260 publications - the 79th percentile of the discipline.
  • 79% of ranked Mathematics scientists score the same or lower than J. William Helton, and about 21% score higher.
  • The median of the discipline falls in the 172–176 publications range, and J. William Helton ranks above the median.
  • The most crowded range is 142–146 publications, holding 112 scientists (3% of the field).
  • 47% of the field sits in the lowest quarter of the value range (up to 162–166 publications), so the distribution leans towards the lower end of the scale.
  • The final bar has no upper bound: it groups every scientist with 537 publications or more, 100 scientists in all (3% of the field).

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.

No. of scientists
50 100 150
Bar chart with 57 bars. Horizontal axis: D-Index, 30 to 86+. Vertical axis: number of scientists, 0 to 174. Most scientists, 174, have 30 D-Index. The last bar groups every scientist with 86 D-Index or more. The highlighted bar, 42 D-Index, is where this scientist sits. 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: 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.

View D-Index distribution as a table
Number of Mathematics scientists by D-index, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
D-Index Scientists This scientist
30 174
31 151
32 174
33 117
34 136
35 127
36 145
37 153
38 150
39 150
40 138
41 136
42 93 42
43 108
44 115
45 112
46 103
47 75
48 59
49 67
50 60
51 57
52 59
53 62
54 60
55 50
56 42
57 54
58 50
59 42
60 41
61 35
62 40
63 21
64 31
65 27
66 29
67 19
68 25
69 17
70 18
71 12
72 14
73 13
74 18
75 9
76 11
77 10
78 9
79 16
80 12
81 10
82 5
83 5
84 13
85 6
86+ 99
Download as CSV

J. William Helton D-index placement in Mathematics in 2026 - data summary

  • The chart plots the discipline H-index (D-index) of all 3,584 Mathematics scientists ranked by Research.com in 2026, grouped into 57 ranges running from 30 to 86+ D-Index.
  • J. William Helton, a Mathematics scholar from University of California, San Diego, records 42 D-Index - the 51st percentile of the discipline.
  • 51% of ranked Mathematics scientists score the same or lower than J. William Helton, and about 49% score higher.
  • The median of the discipline falls in the 42 D-Index range, and J. William Helton falls inside that same range.
  • The most crowded range is 30 D-Index, holding 174 scientists (5% of the field).
  • 58% of the field sits in the lowest quarter of the value range (up to 44 D-Index), so the distribution is heavily right-skewed and high scores are rare.
  • The final bar has no upper bound: it groups every scientist with 86 D-Index or more, 99 scientists in all (3% of the field).

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
Jiawang Nie
Jiawang Nie University of California, San Diego
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
Bruce A. Francis
Bruce A. Francis University of Toronto

External Links

Personal website of J. William Helton

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Best Scientists Citing J. William Helton

Joseph A. Ball

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Virginia Tech

Publications: 77

Mihai Putinar

Mihai Putinar

University of California, Santa Barbara

Publications: 38

Jim Agler

Jim Agler

University of California, San Diego

Publications: 27

Jean B. Lasserre

Jean B. Lasserre

Laboratory for Analysis and Architecture of Systems

Publications: 25

Jiawang Nie

Jiawang Nie

University of California, San Diego

Publications: 22

Daniel Alpay

Daniel Alpay

Chapman University

Publications: 21

Matthew R. James

Matthew R. James

Australian National University

Publications: 19

Roland Speicher

Roland Speicher

Saarland University

Publications: 16

Didier Henrion

Didier Henrion

Laboratory for Analysis and Architecture of Systems

Publications: 14

Vaithilingam Jeyakumar

Vaithilingam Jeyakumar

University of New South Wales

Publications: 14

Allen Tannenbaum

Allen Tannenbaum

Stony Brook University

Publications: 14

Guoyin Li

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Publications: 13

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Publications: 11

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Publications: 11

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Publications: 11

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