World's Best Scientists 2026 revealed!
Richard B. Melrose

Richard B. Melrose

D-Index & Metrics

Mathematics

D-Index
48
Citations
9959
World Ranking
1200
National Ranking
537

Richard B. Melrose publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Richard B. Melrose sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 119 publications — 21st percentile

21% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Richard B. Melrose D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Richard B. Melrose sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 48 D-Index — 67th percentile

67% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Research.com Recognitions

  • 1992 - Fellow of John Simon Guggenheim Memorial Foundation
  • 1986 - Fellow of the American Academy of Arts and Sciences

Overview

Richard B. Melrose is affiliated with MIT in the United States. Their research spans primarily within the field of Mathematics, with additional contributions to Medicine. The main subfields of study include Mathematical Physics, Algebra and Number Theory, Pathology and Forensic Medicine, Computational Theory and Mathematics, and Geometry and Topology.

Their work covers a variety of topics, notably:

  • Homotopy and Cohomology in Algebraic Topology
  • Advanced Topics in Algebra
  • Ophthalmology and Eye Disorders
  • Advanced Operator Algebra Research
  • Matrix Theory and Algorithms
  • Geometric and Algebraic Topology

Melrose has been published frequently in notable venues, including:

  • arXiv (Cornell University)
  • Algebraic & Geometric Topology
  • Advances in Mathematics

Recent papers authored or co-authored by Melrose are:

  • "Generalized Products and Semiclassical Quantization," 2023, arXiv (Cornell University)
  • "Bigerbes," 2021, Algebraic & Geometric Topology
  • "Index and small bundle gerbes," 2023, arXiv (Cornell University)
  • "Equivariant K-theory and Resolution II: Non-Abelian actions," 2020, arXiv (Cornell University)
  • "Index and small bundle gerbes," forthcoming 2025, Advances in Mathematics

Frequent co-authors of Richard B. Melrose include:

  • Panagiotis Dimakis
  • Varghese Mathai
  • Chris Kottke

Richard B. Melrose has received recognition through awards such as:

  • Fellow of the John Simon Guggenheim Memorial Foundation (1992)
  • Fellow of the American Academy of Arts and Sciences (1986)

Best Publications

  • The Atiyah-Patodi-Singer Index Theorem

    Richard B. Melrose

  • Geometric scattering theory

    Richard B. Melrose

  • Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature

    Rafe R Mazzeo;Richard B Melrose

  • Singularities of boundary value problems. I

    R. B. Melrose;J. Sjöstrand

  • Spectral and Scattering Theory for the Laplacian on Asymptotically Euclidian Spaces

    Richard B. Melrose

  • TRANSFORMATION OF BOUNDARY PROBLEMS

    Richard B. Melrose

  • Calculus of conormal distributions on manifolds with corners

    Richard B. Melrose

  • Lagrangian Intersection and the Cauchy Problem

    Richard B. Melrose;Gunther Uhlmann

  • Families of Dirac operators, boundaries and the $b$-calculus

    Richard B. Melrose;Paolo Piazza

  • PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH FIBRED BOUNDARIES

    Rafe Mazzeo;Richard B. Melrose

  • Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle

    Richard B Melrose;Michael E Taylor

  • Equivalence of Glancing Hypersurfaces.

    R. B. Melrose

  • Boundary behavior of the complex Monge-Ampère equation

    John Lee;Richard Melrose

  • The Poisson Summation Formula for Manifolds with Boundary

    Victor Guillemin;Richard Melrose

  • The Propagation of Singularities along Gliding Rays.

    K. G. Andersson;R. B. Melrose

  • Scattering metrics and geodesic flow at infinity

    Richard Melrose;Maciej Zworski

  • Resolvent of the Laplacian on strictly pseudoconvex domains

    C. L. Epstein;R. B. Melrose;G. A. Mendoza

  • Spectral invariants of convex planar regions

    Shahla Marvizi;Richard Melrose

  • Homology of pseudodifferential operators I. Manifolds with boundary

    Richard B. Melrose;Victor Nistor

  • The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration

    Rafe R. Mazzeo;Richard B. Melrose

Frequent Co-Authors

András Vasy
András Vasy Stanford University
Rafe Mazzeo
Rafe Mazzeo Stanford University
Varghese Mathai
Varghese Mathai University of Adelaide
Gunther Uhlmann
Gunther Uhlmann University of Washington
Maciej Zworski
Maciej Zworski University of California, Berkeley
Michael Taylor
Michael Taylor University of North Carolina at Chapel Hill
Daniel S. Freed
Daniel S. Freed The University of Texas at Austin
Jeffrey Rauch
Jeffrey Rauch University of Michigan–Ann Arbor

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