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Topic · Mathematical Physics

Advanced Algebra and Geometry

Advanced Algebra and Geometry is a research topic within Mathematical Physics. Science Explorer counts 27k 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 focuses on providing proofs and related research on the Langlands Conjectures for GL(n) over local and global fields. It encompasses topics such as automorphic forms, representation theory, L-functions, harmonic analysis, algebraic groups, modular forms, symmetric spaces, and cohomology.

  • Langlands Conjectures
  • Automorphic Forms
  • Representation Theory
  • Local Fields
  • L-functions
  • Harmonic Analysis
  • Algebraic Groups
  • Modular Forms
  • Symmetric Spaces
  • Cohomology
Research works
27k
fractional, since 1950
In the world top 10%
2.7k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+26%
the tick is no change
Largest producer
United States
25% of the 10 largest, 2022-now
Advanced Algebra and Geometry

Which countries lead Advanced Algebra and Geometry research?

By volume, the United States and China publish the most (775 and 517 works in 2022-now).

By volume, 2022-now

  1. 1 United States 775 works
  2. 2 China 517 works
  3. 3 France 312 works
  4. 4 Japan 290 works
  5. 5 Germany 270 works
  6. 6 India 226 works
  7. 7 Russia 216 works
  8. 8 United Kingdom 204 works
  9. 9 Italy 152 works
  10. 10 Canada 121 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.

United States: 25.1%China: 16.7%France: 10.1%Japan: 9.4%6 others listed: 38.6%25%largest
United States775 · 25.1%China517 · 16.7%France312 · 10.1%Japan290 · 9.4%6 others listed1,191 · 38.6%

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

Which institutions lead Advanced Algebra and Geometry research?

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

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 158 works
  2. 2 Russian Academy of SciencesRussia 70 works
  3. 3 The University of TokyoJapan 35 works
  4. 4 National Research University Higher School of EconomicsRussia 34 works
  5. 5 Tsinghua UniversityChina 33 works
  6. 6 Kyoto UniversityJapan 32 works
  7. 7 University of MichiganUnited States 28 works
  8. 8 Massachusetts Institute of TechnologyUnited States 27 works
  9. 9 Shandong UniversityChina 26 works
  10. 10 Max Planck SocietyGermany 26 works

Who are the leading researchers in Advanced Algebra and Geometry?

The most-cited researchers publishing on Advanced Algebra and Geometry include Edward H. Witten.

  1. 1 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 Advanced Algebra and Geometry?

The most cited paper in Advanced Algebra and Geometry is "Partial differential equations of parabolic type" (John S. Maybee, 1965), with 3,305 citations. Next come "Algebraic number theory" (2,174) and "Seiberg-Witten Prepotential from Instanton Counting" (1,918).

Most cited papers
#PaperReleasedCitations
1 Partial differential equations of parabolic type John S. Maybee · Journal of the Franklin Institute Jun 1965 3,305
2 Algebraic number theory Kazuya Katô, Nobushige Kurokawa, Takeshi Saito · Translations of mathematical monographs Book chapter 22 Nov 1999 2,174
3 Seiberg-Witten Prepotential from Instanton Counting Nikita Alexandrovich Nekrasov · Advances in Theoretical and Mathematical Physics Open access 2003 1,918
4 Level-spacing distributions and the Airy kernel Craig A. Tracy, Harold Widom · Communications in Mathematical Physics Open access 1994 1,917
5 Phases of N = 2 theories in two dimensions Edward H. Witten · Nuclear Physics B Open access Aug 1993 1,811
All 99 most cited papers, with filters and sorting

Where is Advanced Algebra and Geometry research done?

The largest centres of Advanced Algebra and Geometry research in 2022-now are Moscow (Russia), Beijing (China), Tokyo (Japan) and Paris (France). Among places with at least 20 works in it, it is an unusually large share of all research in Bonn.

Largest cities, 2022-now

  1. 1 MoscowRussia 139 works
  2. 2 BeijingChina 112 works
  3. 3 TokyoJapan 104 works
  4. 4 ParisFrance 102 works
  5. 5 ShanghaiChina 61 works
  6. 6 SeoulSouth Korea 46 works
  7. 7 LondonUnited Kingdom 45 works
  8. 8 BonnGermany 43 works
  9. 9 CambridgeUnited States 41 works
  10. 10 MumbaiIndia 38 works

Where it is the local speciality

  1. BonnDE · 43.2 works15×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Advanced Algebra and Geometry than the world average.

See Advanced Algebra and Geometry on the map

Where is the best place to study Advanced Algebra and Geometry?

Among universities, judged by research, University of Bonn, Princeton University and Massachusetts 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%10%20%30%mean 18.54%fractional works in this field (log) →share of work in the world top 10% →Princeton UniversityUniversity of OxfordUniversity of BonnMassachusetts Instit…
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 BonnGermany 73.819.6%13.9×22 +102.9%
2Princeton UniversityUnited States 73.324.8%9.6×15 +38.7%
3Massachusetts Institute of TechnologyUnited States 68.315.6%11.3×27 -15.4%
4University of OxfordUnited Kingdom 67.022.4%4.1×20 +22.5%
5University of MichiganUnited States 65.513.1%5.4×28 +100.3%
6Harvard UniversityUnited States 65.223.6%1.2×14 +64.8%
7University of California, BerkeleyUnited States 65.123.3%5.2×17 +21.9%
8National Research University Higher School of EconomicsRussia 63.69.0%24.3×34 +31.5%
9Tsinghua UniversityChina 63.613.2%4.1×33 +121.8%
10ETH ZurichSwitzerland 63.020.8%6.6×16 +1.2%

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 Advanced Algebra and Geometry, country by country

Is Advanced Algebra and Geometry research growing?

Output in 2022-2025 was 26% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Advanced Algebra and Geometry.

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 Advanced Algebra and Geometry as a percentage of every work published that year, 0.019% in 2024.

still counting0.020%0.040%0.060%Advanced Algebra and Geometry0.016% in 202519801990200020102020

Fractional works of Advanced Algebra and Geometry 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%Advanced Algebra and Geometry9.7% 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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