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Topic · Applied Mathematics

Algebraic and Geometric Analysis

Algebraic and Geometric Analysis is a research topic within Applied Mathematics. Science Explorer counts 21k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers explores advances in quaternionic analysis, geometric algebra, slice regular functions, dark matter, spinor fields, functional calculus, Clifford analysis, octonions, Dirac operators, and hypercomplex numbers.

  • Quaternionic Analysis
  • Geometric Algebra
  • Slice Regular Functions
  • Dark Matter
  • Spinor Fields
  • Functional Calculus
  • Clifford Analysis
  • Octonions
  • Dirac Operators
  • Hypercomplex Numbers
Research works
21k
fractional, since 1950
In the world top 10%
2.1k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+27%
the tick is no change
Largest producer
China
23% of the 10 largest, 2022-now
Algebraic and Geometric Analysis

Which countries lead Algebraic and Geometric Analysis research?

By volume, China and the United States publish the most (459 and 371 works in 2022-now).

By volume, 2022-now

  1. 1 China 459 works
  2. 2 United States 371 works
  3. 3 Russia 279 works
  4. 4 India 241 works
  5. 5 Germany 134 works
  6. 6 Türkiye 114 works
  7. 7 Italy 109 works
  8. 8 Japan 102 works
  9. 9 France 85 works
  10. 10 Ukraine 80 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: 23.2%United States: 18.8%Russia: 14.1%India: 12.2%6 others listed: 31.6%23%largest
China459 · 23.2%United States371 · 18.8%Russia279 · 14.1%India241 · 12.2%6 others listed624 · 31.6%

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

Which institutions lead Algebraic and Geometric Analysis research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Algebraic and Geometric Analysis research, followed by National Academy of Sciences of Ukraine and Centre National de la Recherche Scientifique.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 70 works
  2. 2 National Academy of Sciences of UkraineUkraine 39 works
  3. 3 Centre National de la Recherche ScientifiqueFrance 38 works
  4. 4 Lomonosov Moscow State UniversityRussia 25 works
  5. 5 Sakai Municipal HospitalJapan 18 works
  6. 6 Politecnico di MilanoItaly 16 works
  7. 7 Chinese Academy of SciencesChina 14 works
  8. 8 Instituto Politécnico NacionalMexico 13 works
  9. 9 University of Hassan II CasablancaMorocco 13 works
  10. 10 Shanghai UniversityChina 13 works

Who are the leading researchers in Algebraic and Geometric Analysis?

The most-cited researchers publishing on Algebraic and Geometric Analysis include Sau Lan Wu and Edward H. Witten.

  1. 1 Sau Lan Wu France 182k citations
  2. 2 Edward H. Witten United States 174k 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 and Geometric Analysis?

The most cited paper in Algebraic and Geometric Analysis is "On Gauge Invariance and Vacuum Polarization" (Julian Schwinger, 1951), with 7,183 citations. Next come "CONTINUOUS INSPECTION SCHEMES" (4,771) and "Pseudoparticle solutions of the Yang-Mills equations" (2,908).

Most cited papers
#PaperReleasedCitations
1 On Gauge Invariance and Vacuum Polarization Julian Schwinger · Physical Review Jun 1951 7,183
2 CONTINUOUS INSPECTION SCHEMES E. S. Page · Biometrika 1954 4,771
3 Pseudoparticle solutions of the Yang-Mills equations Alexander A. Belavin, Alexander M. Polyakov, Arthur S. Schwartz et al. · Physics Letters B Oct 1975 2,908
4 Supergauge transformations in four dimensions Jane A. Wess, Bruno Zumino · Nuclear Physics B Feb 1974 2,706
5 Local phenomenological nucleon-nucleon potentials Roderick V. Reid · Annals of Physics Dec 1968 2,597
All 100 most cited papers, with filters and sorting

Where is Algebraic and Geometric Analysis research done?

The largest centres of Algebraic and Geometric Analysis research in 2022-now are Moscow (Russia), Shanghai (China), Beijing (China) and Kyiv (Ukraine).

Largest cities, 2022-now

  1. 1 MoscowRussia 117 works
  2. 2 ShanghaiChina 41 works
  3. 3 BeijingChina 37 works
  4. 4 KyivUkraine 36 works
  5. 5 TokyoJapan 32 works
  6. 6 Mexico CityMexico 31 works
  7. 7 SeoulSouth Korea 26 works
  8. 8 GuangzhouChina 26 works
  9. 9 ParisFrance 25 works
  10. 10 New DelhiIndia 25 works
See Algebraic and Geometric Analysis on the map

Where is the best place to study Algebraic and Geometric Analysis?

Among universities, judged by research, Shanghai University, Lomonosov Moscow State University and Politecnico di Milano 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%25%50%75%mean 25.57%fractional works in this field (log) →share of work in the world top 10% →Shanghai UniversityLiaocheng UniversityPolitecnico di MilanoLomonosov Moscow Sta…
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
1Shanghai UniversityChina 70.770.8%6.6×13 +157.1%
2Lomonosov Moscow State UniversityRussia 50.06.3%10.5×25 -22.2%
3Politecnico di MilanoItaly 49.436.2%8.2×16 -20.0%
4Liaocheng UniversityChina 49.345.0%18.0×9 +74.9%
5University of NisSerbia 46.121.6%26.6×12 +123.7%
6University of Hassan II CasablancaMorocco 44.515.8%18.4×13 +165.8%
7Chapman UniversityUnited States 44.118.5%64.6×12 +76.9%
8Instituto Politécnico NacionalMexico 40.69.0%13.8×13 +28.7%
9Indian Institute of Science BangaloreIndia 36.624.4%8.7×10 +212.0%
10National Research University Higher School of EconomicsRussia 32.38.1%9.3×10 +21.1%

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 and Geometric Analysis, country by country

Is Algebraic and Geometric Analysis research growing?

Output in 2022-2025 was 27% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Algebraic and Geometric Analysis.

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 and Geometric Analysis as a percentage of every work published that year, 0.014% in 2024.

still counting0.025%0.050%0.075%Algebraic and Geometric Analysis0.014% in 202519801990200020102020

Fractional works of Algebraic and Geometric Analysis 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 and Geometric Analysis11.2% 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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