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Topic · Geometry and Topology

Algebraic Geometry and Number Theory

Algebraic Geometry and Number Theory is a research topic within Geometry and Topology. Science Explorer counts 29k research works in it since 1950. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers a wide range of topics in algebraic geometry and moduli theory, including Gromov-Witten theory, log canonical singularities, motivic cohomology, minimal models, tropical geometry, intersection theory, symplectic geometry, birational geometry, and diophantine equations.

  • Moduli Theory
  • Gromov-Witten Theory
  • Log Canonical Singularities
  • Motivic Cohomology
  • Minimal Models
  • Tropical Geometry
  • Intersection Theory
  • Symplectic Geometry
  • Birational Geometry
  • Diophantine Equations
Research works
29k
fractional, since 1950
In the world top 10%
2.9k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+19%
the tick is no change
Largest producer
United States
26% of the 10 largest, 2022-now
Algebraic Geometry and Number Theory

Which countries lead Algebraic Geometry and Number Theory research?

By volume, the United States and China publish the most (903 and 464 works in 2022-now).

By volume, 2022-now

  1. 1 United States 903 works
  2. 2 China 464 works
  3. 3 France 385 works
  4. 4 Japan 374 works
  5. 5 Germany 324 works
  6. 6 India 285 works
  7. 7 Italy 226 works
  8. 8 United Kingdom 225 works
  9. 9 Russia 156 works
  10. 10 Canada 138 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: 26.0%China: 13.3%France: 11.1%Japan: 10.7%6 others listed: 38.9%26%largest
United States903 · 26.0%China464 · 13.3%France385 · 11.1%Japan374 · 10.7%6 others listed1,354 · 38.9%

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

Which institutions lead Algebraic Geometry and Number Theory research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Algebraic Geometry and Number Theory research, followed by Russian Academy of Sciences and Kyoto University.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 196 works
  2. 2 Russian Academy of SciencesRussia 56 works
  3. 3 Kyoto UniversityJapan 42 works
  4. 4 The University of TokyoJapan 39 works
  5. 5 Tsinghua UniversityChina 37 works
  6. 6 National Research University Higher School of EconomicsRussia 36 works
  7. 7 Max Planck SocietyGermany 32 works
  8. 8 University of MichiganUnited States 29 works
  9. 9 Chinese Academy of SciencesChina 28 works
  10. 10 Sidi Mohamed Ben Abdellah UniversityMorocco 25 works

Who are the leading researchers in Algebraic Geometry and Number Theory?

The most-cited researchers publishing on Algebraic Geometry and Number Theory include Edward H. Witten, B. S. Acharya and O. Schneider.

  1. 1 Edward H. Witten United States 174k citations
  2. 2 B. S. Acharya France 164k citations
  3. 3 O. Schneider Switzerland 141k citations
  4. 4 Hywel C Williams United Kingdom 126k 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 Geometry and Number Theory?

The most cited paper in Algebraic Geometry and Number Theory is "Identity-Based Encryption from the Weil Pairing" (Dan Boneh, Matthew K. Franklin, 2003), with 3,570 citations. Next come "Partial differential equations of parabolic type" (3,305) and "La conjecture de Weil : I" (2,515).

Most cited papers
#PaperReleasedCitations
1 Identity-Based Encryption from the Weil Pairing Dan Boneh, Matthew K. Franklin · SIAM Journal on Computing 2003 3,570
2 Partial differential equations of parabolic type John S. Maybee · Journal of the Franklin Institute Jun 1965 3,305
3 La conjecture de Weil : I Pierre Deligne · Publications mathématiques de l IHÉS 7 Dec 1974 2,515
4 On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I Shing–Tung Yau · Communications on Pure and Applied Mathematics May 1978 2,475
5 Introduction: Motivation Chris Wendl · Cambridge University Press eBooks Book chapter 6 Mar 2020 2,273
All 100 most cited papers, with filters and sorting

Where is Algebraic Geometry and Number Theory research done?

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

Largest cities, 2022-now

  1. 1 ParisFrance 131 works
  2. 2 TokyoJapan 127 works
  3. 3 BeijingChina 121 works
  4. 4 MoscowRussia 111 works
  5. 5 ShanghaiChina 56 works
  6. 6 SeoulSouth Korea 51 works
  7. 7 LondonUnited Kingdom 49 works
  8. 8 BonnGermany 48 works
  9. 9 KyotoJapan 47 works
  10. 10 New YorkUnited States 40 works

Where it is the local speciality

  1. TrentoIT · 24.6 works16×
  2. FesMA · 25.4 works15×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Algebraic Geometry and Number Theory than the world average.

See Algebraic Geometry and Number Theory on the map

Where is the best place to study Algebraic Geometry and Number Theory?

Among universities, judged by research, University of Bonn, Princeton University and Sidi Mohamed Ben Abdellah University 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 16.51%fractional works in this field (log) →share of work in the world top 10% →Princeton UniversityUniversity of BonnSidi Mohamed Ben Abd…University of Warwick
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 65.920.9%12.9×24 +135.3%
2Princeton UniversityUnited States 64.821.6%12.3×22 +4.8%
3Sidi Mohamed Ben Abdellah UniversityMorocco 63.219.4%23.0×25 +108.9%
4University of WarwickUnited Kingdom 61.216.8%11.2×21 +28.4%
5University of MichiganUnited States 60.316.0%4.6×29 +50.8%
6National Research University Higher School of EconomicsRussia 59.110.1%21.9×36 +23.7%
7Massachusetts Institute of TechnologyUnited States 58.824.8%7.1×20 -35.0%
8Kyoto UniversityJapan 57.97.7%13.5×42 -8.0%
9Harvard UniversityUnited States 57.816.9%1.4×18 +68.3%
10Tsinghua UniversityChina 57.210.9%4.0×37 +51.7%

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 Geometry and Number Theory, country by country

Is Algebraic Geometry and Number Theory research growing?

Output in 2022-2025 was 19% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Algebraic Geometry and Number Theory.

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 Geometry and Number Theory as a percentage of every work published that year, 0.018% in 2024.

still counting0.020%0.040%0.060%Algebraic Geometry and Number Theory0.018% in 202519801990200020102020

Fractional works of Algebraic Geometry and Number Theory 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 Geometry and Number Theory9.9% 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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