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. 15.8% 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%
- 4.2k per year above
- Top-10% rate
- 15.8% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- -1% the tick is no change
Which countries lead Advanced Algebra and Geometry research?
By volume, the United States and China publish the most (726 and 464 works in 2022–2025).
By volume, 2022–2025
- 1 United States 726 works
- 2 China 464 works
- 3 France 297 works
- 4 Japan 275 works
- 5 Germany 252 works
- 6 Russia 208 works
- 7 India 203 works
- 8 United Kingdom 193 works
- 9 Italy 143 works
- 10 Canada 114 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.
Shares of the rows listed above, not of the whole node.
Which institutions lead Advanced Algebra and Geometry research?
By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most Advanced Algebra and Geometry research, followed by National Research University Higher School of Economics and The University of Tokyo.
By volume, 2022–2025
- 1 Centre National de la Recherche ScientifiqueFrance 45 works
- 2 National Research University Higher School of EconomicsRussia 33 works
- 3 The University of TokyoJapan 32 works
- 4 Kyoto UniversityJapan 30 works
- 5 Tsinghua UniversityChina 27 works
- 6 University of MichiganUnited States 26 works
- 7 Shandong UniversityChina 25 works
- 8 Massachusetts Institute of TechnologyUnited States 23 works
- 9 Steklov Mathematical InstituteRussia 22 works
- 10 Lomonosov Moscow State UniversityRussia 20 works
Who are the leading researchers in Advanced Algebra and Geometry?
The most-cited researchers publishing on Advanced Algebra and Geometry include Edward Witten, Steven J. Miller and Terence Tao.
- 1 Edward Witten United States 7.2k citations
- 2 Steven J. Miller United States 3.8k citations
- 3 Terence Tao United States 3.1k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Advanced Algebra and Geometry research done?
The largest centres of Advanced Algebra and Geometry research in 2022–2025 are Moscow (Russia), Beijing (China), Paris (France) and Tokyo (Japan). Among places with at least 20 works in it, it is an unusually large share of all research in Bonn.
Largest cities, 2022–2025
Where it is the local speciality
- BonnDE · 38.0 works14×
Location quotient: how much more of its research is in Advanced Algebra and Geometry than the world average.
Where is the best place to study Advanced Algebra and Geometry?
Among universities, judged by research, National Research University Higher School of Economics, Institute of Science and Technology Austria 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.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | National Research University Higher School of EconomicsRussia | 73.7 | 13.7% | 22.1× | 33 | +230.8% |
| 2 | Institute of Science and Technology AustriaAustria | 66.8 | 14.0% | 73.1× | 10 | +258.9% |
| 3 | Massachusetts Institute of TechnologyUnited States | 66.7 | 18.4% | 10.3× | 23 | +22.5% |
| 4 | University of BonnGermany | 65.7 | 21.4% | 15.7× | 19 | -20.1% |
| 5 | Université Paris-SaclayFrance | 65.3 | 13.7% | 9.2× | 13 | +222.5% |
| 6 | Princeton UniversityUnited States | 63.7 | 24.8% | 9.0× | 14 | +8.5% |
| 7 | University of OxfordUnited Kingdom | 61.0 | 26.4% | 4.2× | 19 | +46.7% |
| 8 | Kyoto UniversityJapan | 59.9 | 10.2% | 11.2× | 30 | +39.7% |
| 9 | Leibniz University HannoverGermany | 56.6 | 15.0% | 14.4× | 15 | +22.5% |
| 10 | ETH ZurichSwitzerland | 55.6 | 22.3% | 6.0× | 15 | -12.6% |
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 Algebra and Geometry research growing?
Output in 2018–2022 was 1% lower than in 2013–2017, peaking in 2024. The fastest-growing topics are Advanced Algebra and Geometry.
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.