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Research facility · Rio de Janeiro · Brazil

Instituto Nacional de Matemática Pura e Aplicada

In research, Instituto Nacional de Matemática Pura e Aplicada stands highest in Mathematics (#681 of 1,051 worldwide) and Physical Sciences (#7,674 of 10,670 worldwide), 2022-now. Relative to its size it is most specialised in Geometry and Topology, Mathematical Physics and Mathematics (Geometry and Topology is 116.0× its share of world research).

impa.br/opencms/enROR OpenAlex
World rank, 2022-now
#15,540
of 22,385 · #5,471 all time
Rank in Brazil
#560
of 684
Research works
1.9k
▲ 12% vs 2018-21
Citations
42k
21.5 per fractional work
Top-10% rate
5.2%
all institutions 10.0%
vs its own fields
0.99×
1.00× is exactly expected
Open access
43%
world 40%
International
36%
world 18%
Instituto Nacional de Matemática Pura e Aplicada

What is Instituto Nacional de Matemática Pura e Aplicada known for in research?

The fields where it stands highest, 2022-now, ranked among every institution above the floor in each field.

FieldWorld rankWhere that sitsTop-10% rateWorksAll time
MathematicsField #681 of 1,051 4.8%110 #415
Physical SciencesDomain #7,674 of 10,670 4.5%180 #2582

Each strip is that field's whole ranked pool, with the notch where Instituto Nacional de Matemática Pura e Aplicada sits in it, in the colour of the band that rank falls in. The track under the rate is the rate itself: it carries no average mark, because the average differs by field (from about 6% in Dentistry to 21% in Economics).

Which fields of science does Instituto Nacional de Matemática Pura e Aplicada work in?

In 2022-now, 89% of research at Instituto Nacional de Matemática Pura e Aplicada is in Physical Sciences, 7% in Social Sciences. Its largest fields are Mathematics (55%), Computer Science (13%), Physics and Astronomy (9%). It does 2.2× the world's share of Physical Sciences.

Physical Sciences: 200 fractional works · 88.6% of its workMathematics: 124 fractional works · 54.8% of its workGeometry and Topology: 43 fractional works · 18.9% of its workMathematical Physics: 34 fractional works · 14.9% of its workApplied Mathematics: 23 fractional works · 10.4% of its workAlgebra and Number Theory: 7 fractional works · 3.2% of its workStatistics and Probability: 7 fractional works · 3.0% of its workDiscrete Mathematics and Combinatorics: 5 fractional works · 2.4% of its workNumerical Analysis: 3 fractional works · 1.3% of its workTheoretical Computer Science: 1 fractional works · 0.4% of its workModeling and Simulation: 1 fractional works · 0.3% of its workComputer Science: 30 fractional works · 13.2% of its workComputational Theory and Mathematics: 12 fractional works · 5.5% of its workComputer Graphics and Computer-Aided Design: 5 fractional works · 2.2% of its workComputer Vision and Pattern Recognition: 4 fractional works · 1.9% of its workArtificial Intelligence: 4 fractional works · 1.8% of its workComputer Networks and Communications: 2 fractional works · 1.1% of its workSignal Processing: 1 fractional works · 0.4% of its workHuman-Computer Interaction: 0 fractional works · 0.2% of its workSmaller subfields together: 0 fractional works · 0.2% of its workPhysics and Astronomy: 20 fractional works · 8.8% of its workStatistical and Nonlinear Physics: 9 fractional works · 3.9% of its workCondensed Matter Physics: 7 fractional works · 3.1% of its workAstronomy and Astrophysics: 2 fractional works · 0.9% of its workAtomic and Molecular Physics, and Optics: 2 fractional works · 0.8% of its workNuclear and High Energy Physics: 0 fractional works · 0.2% of its workEngineering: 20 fractional works · 8.7% of its workComputational Mechanics: 8 fractional works · 3.4% of its workControl and Systems Engineering: 3 fractional works · 1.5% of its workOcean Engineering: 2 fractional works · 0.8% of its workElectrical and Electronic Engineering: 2 fractional works · 0.7% of its workCivil and Structural Engineering: 1 fractional works · 0.5% of its workBiomedical Engineering: 1 fractional works · 0.4% of its workAerospace Engineering: 1 fractional works · 0.4% of its workMechanics of Materials: 1 fractional works · 0.4% of its workBuilding and Construction: 1 fractional works · 0.3% of its workMechanical Engineering: 0 fractional works · 0.2% of its workSmaller subfields together: 0 fractional works · 0.2% of its workEarth and Planetary Sciences: 3 fractional works · 1.4% of its workOceanography: 1 fractional works · 0.5% of its workAtmospheric Science: 1 fractional works · 0.5% of its workSmaller subfields together: 1 fractional works · 0.4% of its workEnvironmental Science: 2 fractional works · 1.1% of its workEnvironmental Engineering: 1 fractional works · 0.5% of its workGlobal and Planetary Change: 1 fractional works · 0.3% of its workSmaller subfields together: 0 fractional works · 0.2% of its workMaterials Science: 1 fractional works · 0.6% of its workMaterials Chemistry: 1 fractional works · 0.5% of its workSmaller subfields together: 0 fractional works · 0.1% of its workEnergy: 0 fractional works · 0.0% of its workSocial Sciences: 16 fractional works · 7.3% of its workEconomics, Econometrics and Finance: 7 fractional works · 2.9% of its workFinance: 3 fractional works · 1.5% of its workEconomics and Econometrics: 3 fractional works · 1.2% of its workGeneral Economics, Econometrics and Finance: 0 fractional works · 0.2% of its workDecision Sciences: 3 fractional works · 1.2% of its workManagement Science and Operations Research: 2 fractional works · 0.9% of its workSmaller subfields together: 1 fractional works · 0.3% of its workSocial Sciences: 3 fractional works · 1.2% of its workSociology and Political Science: 1 fractional works · 0.3% of its workEducation: 1 fractional works · 0.3% of its workPolitical Science and International Relations: 0 fractional works · 0.2% of its workSmaller subfields together: 1 fractional works · 0.4% of its workArts and Humanities: 3 fractional works · 1.1% of its workLanguage and Linguistics: 1 fractional works · 0.3% of its workLiterature and Literary Theory: 1 fractional works · 0.3% of its workHistory: 1 fractional works · 0.3% of its workPhilosophy: 1 fractional works · 0.2% of its workSmaller subfields together: 0 fractional works · 0.1% of its workPsychology: 2 fractional works · 0.7% of its workExperimental and Cognitive Psychology: 1 fractional works · 0.3% of its workSmaller subfields together: 1 fractional works · 0.4% of its workBusiness, Management and Accounting: 0 fractional works · 0.2% of its workHealth Sciences: 6 fractional works · 2.6% of its workMedicine: 4 fractional works · 1.9% of its workHealth Informatics: 1 fractional works · 0.4% of its workPediatrics, Perinatology and Child Health: 1 fractional works · 0.3% of its workEpidemiology: 1 fractional works · 0.2% of its workPublic Health, Environmental and Occupational Health: 1 fractional works · 0.2% of its workSmaller subfields together: 2 fractional works · 0.7% of its workHealth Professions: 1 fractional works · 0.7% of its workGeneral Health Professions: 1 fractional works · 0.5% of its workSmaller subfields together: 0 fractional works · 0.2% of its workNursing: 0 fractional works · 0.0% of its workLife Sciences: 3 fractional works · 1.4% of its workBiochemistry, Genetics and Molecular Biology: 2 fractional works · 0.8% of its workCell Biology: 1 fractional works · 0.4% of its workSmaller subfields together: 1 fractional works · 0.4% of its workAgricultural and Biological Sciences: 1 fractional works · 0.6% of its workPlant Science: 0 fractional works · 0.2% of its workSmaller subfields together: 1 fractional works · 0.4% of its workNeuroscience: 0 fractional works · 0.1% of its workALL ITS WORKInstitutoNacional de…226fractional works, 2022-now
Life Sciences1%Physical Sciences89%Health Sciences3%Social Sciences7%

Each ring splits the one inside it: the four domains of science, their fields, their subfields. Size is fractional works in 2022-now. Every slice is a page; the interactive view zooms down to single topics and colours each by how much more of it this institution does than the world.

Its 4 domains and 20 fields, with their numbers
    1. Mathematics12454.8%
    2. Computer Science3013.2%
    3. Physics and Astronomy208.8%
    4. Engineering208.7%
    5. Earth and Planetary Sciences31.4%
    6. Environmental Science21.1%
    7. Materials Science10.6%
    8. Energy00.0%
    1. Economics, Econometrics and Finance72.9%
    2. Decision Sciences31.2%
    3. Social Sciences31.2%
    4. Arts and Humanities31.1%
    5. Psychology20.7%
    6. Business, Management and Accounting00.2%
    1. Medicine41.9%
    2. Health Professions10.7%
    3. Nursing00.0%
    1. Biochemistry, Genetics and Molecular Biology20.8%
    2. Agricultural and Biological Sciences10.6%
    3. Neuroscience00.1%
All of science, and how each field's share has moved since 1950: the Science domain explorer

What does Instituto Nacional de Matemática Pura e Aplicada specialise in?

Where its research is concentrated relative to its size: Geometry and Topology takes 116.0× the share of its output that it takes of world research.

  1. Geometry and TopologySubfield · 42.6 works116×
  2. Mathematical PhysicsSubfield · 33.6 works94×
  3. MathematicsField · 123.7 works47×
  4. Applied MathematicsSubfield · 23.4 works36×
← less than its size predicts1×more →

Location quotient, a volume reading rather than an impact one. It surfaces small, lopsided specialities.

Field profile

Location quotient across every field it publishes in: outside the ring is more than an institution of this size would be expected to publish, inside it is less.

Agricultural and Biological Sciences: 0.12× its world share, 1 worksAgricultural and Bio…Biochemistry, Genetics and Molecular Biology: 0.15× its world share, 2 worksBiochemistry, Geneti…Neuroscience: 0.07× its world share, 0 worksNeuroscienceComputer Science: 1.70× its world share, 30 worksComputer ScienceEarth and Planetary Sciences: 0.87× its world share, 3 worksEarth and Planetary …Energy: 0.04× its world share, 0 worksEnergyEngineering: 0.58× its world share, 20 worksEngineeringEnvironmental Science: 0.22× its world share, 2 worksEnvironmental ScienceMaterials Science: 0.18× its world share, 1 worksMaterials ScienceMathematics: 46.60× its world share, 124 worksMathematicsPhysics and Astronomy: 3.96× its world share, 20 worksPhysics and AstronomyHealth Professions: 0.25× its world share, 2 worksHealth ProfessionsMedicine: 0.10× its world share, 4 worksMedicineNursing: 0.05× its world share, 0 worksNursingArts and Humanities: 0.40× its world share, 3 worksArts and HumanitiesBusiness, Management and Accounting: 0.06× its world share, 0 worksBusiness, Management…Decision Sciences: 1.20× its world share, 3 worksDecision SciencesEconomics, Econometrics and Finance: 1.38× its world share, 7 worksEconomics, Econometr…Psychology: 0.22× its world share, 2 worksPsychologySocial Sciences: 0.09× its world share, 3 worksSocial Sciences1×world share
more than its size predictsabout as predictedless

Rings at 0.5×, 1× and 2×. Widest outward: Mathematics, 46.6×. Every wedge is a field page.

All 20 fields, with their numbers
  1. Mathematics46.60×124 works
  2. Physics and Astronomy3.96×20 works
  3. Computer Science1.70×30 works
  4. Economics, Econometrics and Finance1.38×7 works
  5. Decision Sciences1.20×3 works
  6. Earth and Planetary Sciences0.87×3 works
  7. Engineering0.58×20 works
  8. Arts and Humanities0.40×3 works
  9. Health Professions0.25×2 works
  10. Environmental Science0.22×2 works
  11. Psychology0.22×2 works
  12. Materials Science0.18×1 works
  13. Biochemistry, Genetics and Molecular Biology0.15×2 works
  14. Agricultural and Biological Sciences0.12×1 works
  15. Medicine0.10×4 works
  16. Social Sciences0.09×3 works
  17. Neuroscience0.07×0 works
  18. Business, Management and Accounting0.06×0 works
  19. Nursing0.05×0 works
  20. Energy0.04×0 works

Who are the top researchers at Instituto Nacional de Matemática Pura e Aplicada?

Ranked on the quality score, Benar Fux Svaiter, Marcelo Viana and Artur Avila lead among researchers whose main affiliation is Instituto Nacional de Matemática Pura e Aplicada.

  1. 1 Benar Fux Svaiter Brazil · #180,789 worldwide 9.5k citations · 171 works
  2. 2 Marcelo Viana Brazil · #235,549 worldwide 4.9k citations · 138 works
  3. 3 Artur Avila Brazil · #240,694 worldwide 3.4k citations · 159 works
  4. 4 Ricardo Mañé Brazil · #360,696 worldwide 5k citations · 51 works
  5. 5 Robert Morris Brazil · #370,243 worldwide 3.3k citations · 184 works
  6. 6 Claudia A. Sagastizábal Brazil · #383,083 worldwide 4.8k citations · 152 works
  7. 7 Mikhail V. Solodov Brazil · #455,661 worldwide 5.3k citations · 136 works
  8. 8 Alfredo Noel Iusem Brazil · #463,368 worldwide 6.4k citations · 172 works
  9. 9 Jacob Palis Brazil · #485,727 worldwide 5.3k citations · 92 works
  10. 10 Emanuel Carneiro Brazil · #599,478 worldwide 1k citations · 74 works
All ranked researchers at Instituto Nacional de Matemática Pura e Aplicada

What are the most cited papers from Instituto Nacional de Matemática Pura e Aplicada?

The most cited paper from Instituto Nacional de Matemática Pura e Aplicada is "Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods" (Hédy Attouch, Jérôme Bolte, Benar Fux Svaiter, 2011), with 1,494 citations. Next come "Dynamically encircling an exceptional point for asymmetric mode switching" (1,095) and "Singularities of vector fields" (710).

Most cited papers
#PaperReleasedCitations
1 Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods Hédy Attouch, Jérôme Bolte, Benar Fux Svaiter · Mathematical Programming 19 Aug 2011 1,494
2 Dynamically encircling an exceptional point for asymmetric mode switching Jörg Doppler, Alexei A. Mailybaev, Julian Böhm et al. · Nature Open access 22 Jul 2016 1,095
3 Singularities of vector fields Floris Takens · Publications mathématiques de l IHÉS 7 Dec 1974 710
4 Steepest descent methods for multicriteria optimization Jörg Fliege, Benar Fux Svaiter · Mathematical Methods of Operations Research 17 Aug 2000 664
5 Rational Asset Pricing Bubbles Manuel S. Santos, Michael Woodford · Econometrica 1997 586
All 58 most cited papers, with filters and sorting

Which keywords describe research at Instituto Nacional de Matemática Pura e Aplicada?

By fractional works in 2022-now, weighted toward what it does more of than the world: Symplectic Geometry, Tropical Geometry, Dynamical Systems, Optimal Transport, Ricci Curvature, Approximation Algorithms, Stability and Gromov-Witten Theory.

▲ more of its work than of the world's◆ about the world's share▼ less than the world's

Size is fractional works in 2022-now in the topics tagged with each word; colour is the word's share of this institution's work against its share of the world's. The 40 words are chosen for being large and distinctive. Each links to the topic it comes from most.

All 40 words, with their numbers
  1. Symplectic Geometry15▲ 181×2 topics
  2. Tropical Geometry11▲ 152×2 topics
  3. Dynamical Systems10▲ 65×3 topics
  4. Approximation Algorithms10▲ 58×5 topics
  5. Optimal Transport10▲ 204×1 topic
  6. Ricci Curvature10▲ 204×1 topic
  7. Stability10▲ 19×2 topics
  8. Gromov-Witten Theory9▲ 207×1 topic
  9. Kähler Metrics9▲ 304×1 topic
  10. Moduli Theory9▲ 207×1 topic
  11. Scalar Curvature9▲ 304×1 topic
  12. Monte Carlo Simulation9▲ 19×4 topics
  13. Ergodic Theory9▲ 136×2 topics
  14. Cohomology8▲ 91×2 topics
  15. Phase Transitions8▲ 61×3 topics
  16. Chaos8▲ 48×1 topic
  17. Fractals8▲ 203×1 topic
  18. K-Theory8▲ 132×2 topics
  19. Fractal Dimension7▲ 89×2 topics
  20. Knot Invariants7▲ 210×1 topic
  21. Symplectic Topology7▲ 210×1 topic
  22. Interacting Particle Systems7▲ 252×1 topic
  23. Scaling Limits7▲ 252×1 topic
  24. Critical Phenomena7▲ 148×1 topic
  25. Random Walk Algorithm7▲ 148×1 topic
  26. Nonlinear Equations6▲ 20×5 topics
  27. Quantum Groups6▲ 75×2 topics
  28. Deformation Quantization6▲ 152×1 topic
  29. Modular Forms6▲ 69×3 topics
  30. Poisson Manifolds6▲ 152×1 topic
  31. Inverse Problems6▲ 23×4 topics
  32. Holomorphic Functions6▲ 96×2 topics
  33. L-Functions5▲ 86×2 topics
  34. Model Selection5▲ 26×3 topics
  35. Representation Theory5▲ 72×2 topics
  36. Bifurcations5▲ 89×1 topic
  37. Planar Systems5▲ 171×1 topic
  38. Automorphic Forms5▲ 122×1 topic
  39. Langlands Conjectures5▲ 122×1 topic
  40. Nonlinear Schrödinger Equation4▲ 34×2 topics

Which research topics does Instituto Nacional de Matemática Pura e Aplicada publish most on?

By volume in 2022-now: Geometric Analysis and Curvature Flows, Geometry and complex manifolds, Algebraic Geometry and Number Theory and Mathematical Dynamics and Fractals.

Geometric Analysis and C…10Geometric Analysis and Curvature Flows: 10 fractional worksGeometry and complex man…9Geometry and complex manifolds: 9 fractional worksAlgebraic Geometry and Number Theory: 9 fractional worksMathematical Dynamics an…8Mathematical Dynamics and Fractals: 8 fractional worksGeometric and Algebraic …7Geometric and Algebraic Topology: 7 fractional worksStochastic processes and statistical mechanics: 7 fractional worksTheoretical and Computational Physics: 7 fractional worksHomotopy and Cohomology …6Homotopy and Cohomology in Algebraic Topology: 6 fractional worksAdvanced Differential Equations and Dynamical Systems: 5 fractional worksAdvanced Algebra and Geometry: 5 fractional works
Applied MathematicsGeometry and TopologyMathematical PhysicsCondensed Matter Physics

Area is fractional works; colour is the subfield each topic belongs to.

  1. 1 Geometric Analysis and Curvature Flows Applied Mathematics 10 works
  2. 2 Geometry and complex manifolds Geometry and Topology 9 works
  3. 3 Algebraic Geometry and Number Theory Geometry and Topology 9 works
  4. 4 Mathematical Dynamics and Fractals Mathematical Physics 8 works
  5. 5 Geometric and Algebraic Topology Geometry and Topology 7 works
  6. 6 Stochastic processes and statistical mechanics Mathematical Physics 7 works
  7. 7 Theoretical and Computational Physics Condensed Matter Physics 7 works
  8. 8 Homotopy and Cohomology in Algebraic Topology Mathematical Physics 6 works
  9. 9 Advanced Differential Equations and Dynamical Systems Geometry and Topology 5 works
  10. 10 Advanced Algebra and Geometry Mathematical Physics 5 works

How open and international is its research?

Against the world's own shares: the tick on each track. Both are shares of its output, so they sit on one scale and can be read against each other as well as against the world.

openly available42.6%not open57.4%

World: 40% of research is openly available.

with international co-authors36.3%domestic only63.7%

World: 18% is written across borders.

How has Instituto Nacional de Matemática Pura e Aplicada's research output changed?

Output in 2022-2025 was 12% higher than in 2018-2021.

still counting1990200020102020
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 Instituto Nacional de Matemática Pura e Aplicada as a percentage of every work published that year, 0.0012% in 2024.

still counting0.0025%0.0050%0.0075%Instituto Nacional de Matemática Pura e Aplicada0.00083% in 202519801990200020102020

Fractional works of Instituto Nacional de Matemática Pura e Aplicada 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, against all institutions in the same year.

still counting10%20%all institutions10.0% in 2025Instituto Nacional de Matemática Pura e Aplicada6.3% in 2025200020102020

Of each year's output, the share that reached the world's 10% most cited for its field and year. Peak 19.2% in 2012.

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Instituto Nacional de Matemática Pura e Aplicada on Science Explorer

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