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advanced mathematical theories

advanced mathematical theories is a research topic within Mathematical Physics. Science Explorer counts 18k 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 the application of p-adic numbers and ultrametric spaces in mathematical physics, particularly in areas such as string theory, dynamics, wavelets, nonlinear equations, and Gibbs measures. It explores the implications of p-adic models in understanding phenomena in ultrametric spaces and their relevance to mathematical physics.

  • p-adic
  • mathematical physics
  • ultrametric
  • dynamics
  • string theory
  • wavelets
  • nonlinear equations
  • Gibbs measures
  • quantization
  • ergodic theory
Research works
18k
fractional, since 1950
In the world top 10%
1.9k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+14%
the tick is no change

Which countries lead advanced mathematical theories research?

By volume, Russia and the United States publish the most (387 and 269 works in 2022–2025).

By volume, 2022–2025

  1. 1 Russia 387 works
  2. 2 United States 269 works
  3. 3 China 258 works
  4. 4 India 133 works
  5. 5 France 109 works
  6. 6 Germany 87 works
  7. 7 Japan 86 works
  8. 8 Ukraine 75 works
  9. 9 Italy 74 works
  10. 10 United Kingdom 58 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.

Russia: 25.2%United States: 17.5%China: 16.8%India: 8.6%6 others listed: 31.8%25%largest
Russia387 · 25.2%United States269 · 17.5%China258 · 16.8%India133 · 8.6%6 others listed489 · 31.8%

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

Which institutions lead advanced mathematical theories research?

By volume in 2022–2025, Lomonosov Moscow State University publishes the most advanced mathematical theories research, followed by Steklov Mathematical Institute and Russian Academy of Sciences.

Who are the leading researchers in advanced mathematical theories?

The most-cited researchers publishing on advanced mathematical theories include Κ. Peters, S. A. Çetin and A. Zhemchugov.

  1. 1 Κ. Peters United Kingdom 7.8k citations
  2. 2 S. A. Çetin China 7.2k citations
  3. 3 A. Zhemchugov China 7.2k citations
  4. 4 V. Kartvelishvili Israel 6.8k citations

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

Where is advanced mathematical theories research done?

The largest centres of advanced mathematical theories research in 2022–2025 are Moscow (Russia), Beijing (China), Paris (France) and Tashkent (Uzbekistan). Among places with at least 20 works in it, it is an unusually large share of all research in Yerevan and Tashkent.

Largest cities, 2022–2025

  1. 1 Moscow Russia 175 works
  2. 2 Beijing China 42 works
  3. 3 Paris France 38 works
  4. 4 Tashkent Uzbekistan 32 works
  5. 5 Kyiv Ukraine 30 works
  6. 6 Saint Petersburg Russia 28 works
  7. 7 Yerevan Armenia 27 works
  8. 8 Tokyo Japan 27 works
  9. 9 Nanjing China 20 works
  10. 10 Novosibirsk Russia 20 works

Where it is the local speciality

  1. YerevanAM · 26.9 works25×
  2. TashkentUZ · 31.6 works10×
← less than its size predictsmore →

Location quotient: how much more of its research is in advanced mathematical theories than the world average.

See advanced mathematical theories on the map

Where is the best place to study advanced mathematical theories?

Among universities, judged by research, Lomonosov Moscow State University, Moscow Center For Continuous Mathematical Education and National University of Uzbekistan 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%5%10%mean 6.58%fractional works in this node (log) →share in the world top 10% →Lomonosov Moscow State University: 47, 11.3%Moscow Center For Continuous Mathematical Education: 9, 11.5%National University of Uzbekistan: 9, 10.4%Yerevan State University: 12, 3.8%Indian Statistical Institute: 8, 8.9%Saratov State University: 9, 7.6%National Research University Higher School of Economics: 10, 2.9%St Petersburg University: 17, 1.5%University of California San Diego: 11, 6.2%University of Sfax: 10, 1.7%Moscow Center For Co…Lomonosov Moscow Sta…National University …Yerevan State Univer…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Lomonosov Moscow State UniversityRussia 82.811.3%23.2×47 +40.0%
2 Moscow Center For Continuous Mathematical EducationRussia 64.111.5%217.8×9
3 National University of UzbekistanUzbekistan 62.410.4%24.1×9 +92.8%
4 Yerevan State UniversityArmenia 55.43.8%53.2×12 +238.6%
5 Indian Statistical InstituteIndia 50.78.9%43.0×8 -36.8%
6 Saratov State UniversityRussia 48.17.6%43.7×9 -4.7%
7 National Research University Higher School of EconomicsRussia 43.82.9%10.9×10 +72.5%
8 St Petersburg UniversityRussia 43.71.5%14.8×17 +48.8%
9 University of California San DiegoUnited States 42.66.2%5.4×11 +225.3%
10 University of SfaxTunisia 42.11.7%16.8×10 +69.7%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is advanced mathematical theories research growing?

Output in 2018–2022 was 14% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are advanced mathematical theories.

19801990200020102020
grewheldshrank

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

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.