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Topic · Geometry and Topology

Algebraic structures and combinatorial models

Algebraic structures and combinatorial models is a research topic within Geometry and Topology. Science Explorer counts 42k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers explores the interplay between cluster algebras and triangulated categories, with a focus on derived categories, quiver representations, and homological dimensions. It also delves into topics such as quantum groups, Calabi-Yau algebras, modular tensor categories, and their connections to conformal field theory and Kac-Moody algebras.

  • Cluster Algebras
  • Triangulated Categories
  • Derived Categories
  • Quiver Representations
  • Homological Dimensions
  • Quantum Groups
  • Calabi-Yau Algebras
  • Modular Tensor Categories
  • Conformal Field Theory
  • Kac-Moody Algebras
Research works
42k
fractional, since 1950
In the world top 10%
4.2k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+10%
the tick is no change
Largest producer
China
27% of the 10 largest, 2022-now
Algebraic structures and combinatorial models

Which countries lead Algebraic structures and combinatorial models research?

By volume, China and the United States publish the most (1.2k and 959 works in 2022-now).

By volume, 2022-now

  1. 1 China 1.2k works
  2. 2 United States 959 works
  3. 3 Japan 364 works
  4. 4 Germany 320 works
  5. 5 India 320 works
  6. 6 United Kingdom 315 works
  7. 7 France 308 works
  8. 8 Russia 289 works
  9. 9 Italy 214 works
  10. 10 Canada 142 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 26.6%United States: 21.8%Japan: 8.3%Germany: 7.3%6 others listed: 36.1%27%largest
China1,173 · 26.6%United States959 · 21.8%Japan364 · 8.3%Germany320 · 7.3%6 others listed1,588 · 36.1%

Shares of the rows listed above, not of the whole node.

Which institutions lead Algebraic structures and combinatorial models research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Algebraic structures and combinatorial models research, followed by Russian Academy of Sciences and The University of Tokyo.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 152 works
  2. 2 Russian Academy of SciencesRussia 87 works
  3. 3 The University of TokyoJapan 56 works
  4. 4 Tsinghua UniversityChina 45 works
  5. 5 Max Planck SocietyGermany 44 works
  6. 6 Chinese Academy of SciencesChina 36 works
  7. 7 University of OxfordUnited Kingdom 35 works
  8. 8 Massachusetts Institute of TechnologyUnited States 33 works
  9. 9 National Research University Higher School of EconomicsRussia 32 works
  10. 10 Kyoto UniversityJapan 32 works

Who are the leading researchers in Algebraic structures and combinatorial models?

The most-cited researchers publishing on Algebraic structures and combinatorial models include John C. Morris, Kenji Watanabe and Harry Eugene Stanley.

  1. 1 John C. Morris United States 241k citations
  2. 2 Kenji Watanabe Japan 237k citations
  3. 3 Harry Eugene Stanley United States 198k citations
  4. 4 Edward H. Witten United States 174k citations
  5. 5 B. S. Acharya France 164k citations
  6. 6 Minghui Liu France 137k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Algebraic structures and combinatorial models?

The most cited paper in Algebraic structures and combinatorial models is "The Magma Algebra System I: The User Language" (Wieb Bosma, John Cannon, Catherine Playoust, 1997), with 7,465 citations. Next come "Infinite conformal symmetry in two-dimensional quantum field theory" (4,909) and "The density-matrix renormalization group in the age of matrix product states" (4,199).

Most cited papers
#PaperReleasedCitations
1 The Magma Algebra System I: The User Language Wieb Bosma, John Cannon, Catherine Playoust · Journal of Symbolic Computation Open access Sep 1997 7,465
2 Infinite conformal symmetry in two-dimensional quantum field theory Alexander A. Belavin, Andrey Polyakov, A. B. Zamolodchikov · Nuclear Physics B Jul 1984 4,909
3 The density-matrix renormalization group in the age of matrix product states Ulrich Schollwöck · Annals of Physics Open access 2 Oct 2010 4,199
4 String Theory and Noncommutative Geometry Nathan Seiberg, Edward H. Witten Preprint 1999 3,217
5 Microscopic origin of the Bekenstein-Hawking entropy Andrew Strominger, Cumrun Vafa · Physics Letters B Open access Jun 1996 3,090
All 100 most cited papers, with filters and sorting

Where is Algebraic structures and combinatorial models research done?

The largest centres of Algebraic structures and combinatorial models research in 2022-now are Beijing (China), Moscow (Russia), Tokyo (Japan) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Aligarh.

Largest cities, 2022-now

  1. 1 BeijingChina 180 works
  2. 2 MoscowRussia 168 works
  3. 3 TokyoJapan 135 works
  4. 4 ShanghaiChina 125 works
  5. 5 ParisFrance 106 works
  6. 6 NanjingChina 66 works
  7. 7 LondonUnited Kingdom 54 works
  8. 8 PragueCzechia 51 works
  9. 9 BonnGermany 49 works
  10. 10 CambridgeUnited States 49 works

Where it is the local speciality

  1. AligarhIN · 29.6 works15×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Algebraic structures and combinatorial models than the world average.

See Algebraic structures and combinatorial models on the map

Where is the best place to study Algebraic structures and combinatorial models?

Among universities, judged by research, University of Oxford, The University of Tokyo and California Institute of Technology score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 25.02%fractional works in this field (log) →share of work in the world top 10% →California Institute…Princeton UniversityUniversity of OxfordThe University of To…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1University of OxfordUnited Kingdom 72.729.4%4.6×35 +31.6%
2The University of TokyoJapan 70.821.1%8.2×56 +25.1%
3California Institute of TechnologyUnited States 67.342.9%6.7×13 +10.3%
4Princeton UniversityUnited States 62.736.1%5.5×13 +2.5%
5Uppsala UniversitySweden 59.017.8%6.9×20 +38.9%
6Tsinghua UniversityChina 58.212.4%3.6×45 +87.7%
7Massachusetts Institute of TechnologyUnited States 57.615.3%8.8×33 -10.3%
8Zhejiang Normal UniversityChina 57.426.5%10.2×16 +63.8%
9University of TriesteItaly 54.831.1%9.7×10 +60.0%
10Utrecht UniversityNetherlands 54.317.6%3.9×15 +89.3%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Algebraic structures and combinatorial models, country by country

Is Algebraic structures and combinatorial models research growing?

Output in 2022-2025 was 10% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Algebraic structures and combinatorial models.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Algebraic structures and combinatorial models as a percentage of every work published that year, 0.026% in 2024.

still counting0.025%0.050%0.075%Algebraic structures and combinatorial models0.022% in 202519801990200020102020

Fractional works of Algebraic structures and combinatorial models over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Algebraic structures and combinatorial models9.7% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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