2026 Richard B. Melrose: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	48	1200	1026	536	424	119	9959

Discipline name

D-Index

World Ranking

Current World Ranking

National Ranking

Current National Ranking

Publications

Citations

Mathematics

1200

1026

536

424

119

9959

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

1495
Citations
Geometric scattering theory

Richard B. Melrose

661
Citations
Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature

Rafe R Mazzeo;Richard B Melrose

560
Citations
Singularities of boundary value problems. I

R. B. Melrose;J. Sjöstrand

547
Citations
Spectral and Scattering Theory for the Laplacian on Asymptotically Euclidian Spaces

Richard B. Melrose

372
Citations
TRANSFORMATION OF BOUNDARY PROBLEMS

Richard B. Melrose

290
Citations
Calculus of conormal distributions on manifolds with corners

Richard B. Melrose

283
Citations
Lagrangian Intersection and the Cauchy Problem

Richard B. Melrose;Gunther Uhlmann

248
Citations
Families of Dirac operators, boundaries and the $b$-calculus

Richard B. Melrose;Paolo Piazza

232
Citations
PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH FIBRED BOUNDARIES

Rafe Mazzeo;Richard B. Melrose

229
Citations
Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle

Richard B Melrose;Michael E Taylor

201
Citations
Equivalence of Glancing Hypersurfaces.

R. B. Melrose

193
Citations
Boundary behavior of the complex Monge-Ampère equation

John Lee;Richard Melrose

187
Citations
The Poisson Summation Formula for Manifolds with Boundary

Victor Guillemin;Richard Melrose

185
Citations
The Propagation of Singularities along Gliding Rays.

K. G. Andersson;R. B. Melrose

185
Citations
Scattering metrics and geodesic flow at infinity

Richard Melrose;Maciej Zworski

182
Citations
Resolvent of the Laplacian on strictly pseudoconvex domains

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

174
Citations
Spectral invariants of convex planar regions

Shahla Marvizi;Richard Melrose

143
Citations
Homology of pseudodifferential operators I. Manifolds with boundary

Richard B. Melrose;Victor Nistor

140
Citations
The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration

Rafe R. Mazzeo;Richard B. Melrose

134
Citations

Frequent Co-Authors

András Vasy Stanford University

Rafe Mazzeo Stanford University

Varghese Mathai University of Adelaide

Isadore Manuel Singer MIT

Gunther Uhlmann University of Washington

Maciej Zworski University of California, Berkeley

Victor Guillemin MIT

Michael Taylor University of North Carolina at Chapel Hill

Daniel S. Freed The University of Texas at Austin

Jeffrey Rauch University of Michigan–Ann Arbor

External Links

Wikipedia of Richard B. Melrose Personal website of Richard B. Melrose

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