Richard Burt Melrose
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Australian mathematician
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Mathematics
Richard Burt Melrose's Degrees
- Bachelors Mathematics University of Melbourne
- Masters Mathematics University of Melbourne
- PhD Mathematics University of Melbourne
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Why Is Richard Burt Melrose Influential?
(Suggest an Edit or Addition)According to Wikipedia, Richard Burt Melrose is an Australian mathematician and professor at the Massachusetts Institute of Technology who works on geometric analysis, partial differential equations, and differential geometry.
Richard Burt Melrose's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- The Atiyah-Patodi-Singer Index Theorem (1993) (982)
- Geometric Scattering Theory (1995) (491)
- Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature (1987) (455)
- Singularities of boundary value problems. I (1978) (283)
- Transformation of boundary problems (1981) (192)
- Lagrangian Intersection and the Cauchy Problem (1979) (182)
- Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle (1985) (164)
- PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH FIBRED BOUNDARIES (1998) (163)
- Families of Dirac operators, boundaries and the $b$-calculus (1997) (157)
- Calculus of conormal distributions on manifolds with corners (1992) (155)
- Spectral and Scattering Theory for the Laplacian on Asymptotically Euclidian Spaces (2020) (147)
- Singularities and energy decay in acoustical scattering (1979) (139)
- Resolvent of the Laplacian on strictly pseudoconvex domains (1991) (135)
- Scattering metrics and geodesic flow at infinity (1996) (133)
- Equivalence of glancing hypersurfaces (1976) (130)
- The Poisson Summation Formula for Manifolds with Boundary (1979) (127)
- The propagation of singularities along gliding rays (1977) (126)
- Boundary behavior of the complex Monge-Ampère equation (1982) (126)
- Homology of pseudodifferential operators I. Manifolds with boundary (1996) (113)
- The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration (1990) (108)
- Spectral invariants of convex planar regions (1982) (99)
- Microlocal parametrices for diffractive boundary value problems (1975) (98)
- Analytic K-theory on manifolds with corners (1992) (91)
- Pseudodifferential operators, corners and singular limits (1990) (91)
- Polynomial bound on the number of scattering poles (1983) (89)
- Scattering theory and the trace of the wave group (1982) (87)
- Interaction of nonlinear progressing waves for semilinear wave equations (1985) (83)
- An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary (1997) (80)
- Asymptotics of Solutions of the Wave Equation on de Sitter-Schwarzschild Space (2008) (79)
- The eta invariant and families of pseudodifferential operators (1995) (76)
- Elliptic Operators of Totally Characteristic Type (1983) (73)
- Propagation for the Wave Group of a Positive Subelliptic Second-Order Differential Operator (1986) (70)
- Propagation of singularities for the wave equation on conic manifolds (2004) (68)
- Analytic surgery and the accumulation of eigenvalues (1995) (67)
- Weyl asymptotics for the phase in obstacle scattering (1988) (66)
- K-theory of C*-algebras of b-pseudodifferential Operators (1998) (58)
- Analytic surgery and the eta invariant (1995) (56)
- The wave front set of the solution of a simple initial-boundary value problem with glancing rays. II (1977) (54)
- Spectral and scattering theory for symbolic potentials of order zero (2001) (52)
- Weyl''s conjecture for manifolds with concave boundary (1980) (50)
- Polynomial bound on the distribution of poles in scattering by an obstacle (1984) (48)
- CONTACT DEGREE AND THE INDEX OF FOURIER INTEGRAL OPERATORS (1998) (42)
- FRACTIONAL ANALYTIC INDEX (2004) (41)
- Interaction of progressing waves for semilinear wave equations. II (1987) (40)
- INDEX IN K-THEORY FOR FAMILIES OF FIBRED CUSP OPERATORS (2005) (40)
- The index of projective families of elliptic operators: the decomposable case (2002) (39)
- A signature formula for manifolds with corners of codimension two (1997) (39)
- An inverse spectral result for elliptical regions in R2 (1979) (39)
- Analytic Continuation and Semiclassical Resolvent Estimates on Asymptotically Hyperbolic Spaces (2011) (39)
- Microlocal structure of involutive conical refraction (1979) (39)
- The Cauchy problem for effectively hyperbolic operators (1983) (38)
- Propagation of singularities for the wave equation on edge manifolds (2001) (38)
- Generalized blow-up of corners and fiber products (2011) (30)
- Equivalence of glancing hypersurfaces. II (1981) (29)
- Local Fourier-Airy integral operators (1975) (28)
- Forward scattering by a convex obstacle (1980) (28)
- FAMILIES INDEX FOR PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH BOUNDARY (2003) (27)
- A Cohomological Invariant of Discrete Dynamical Systems (1981) (27)
- The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two (1984) (27)
- The inverse spectral problem for planar domains (1996) (26)
- Microlocal propagation near radial points and scattering for symbolic potentials of order zero (2005) (26)
- Diffraction of singularities for the wave equation on manifolds with corners (2009) (24)
- The radiation pattern of a diffracted wave near the shadow boundary (1986) (24)
- Fibrations, compactifications and algebras of pseudodifferential operators (1996) (23)
- The Wave Equation in A Wedge With General Boundary Conditions (1992) (21)
- Fredholm realizations of elliptic symbols on manifolds with boundary (2006) (16)
- Star products and local line bundles (2007) (16)
- Isospectral sets of drumheads are compact in C (2007) (15)
- A modk index theorem (1992) (15)
- Equivariant and fractional index of projective elliptic operators (2006) (14)
- Generalized backscattering and the Lax-Phillips transform (2007) (14)
- C*-algebras and elliptic theory (2006) (14)
- Elliptic boundary problems on spaces with conic points (1981) (14)
- The Cauchy Problem and Propagation of Singularities (1984) (13)
- Boundary behaviour of Weil-Petersson and fiber metrics for Riemann moduli spaces (2016) (12)
- Semilinear waves with cusp singularities (1987) (11)
- Normal self-intersections of the characteristic variety (1975) (11)
- Scattering configuration spaces (2008) (10)
- Equivalence of string and fusion loop-spin structures (2013) (9)
- Scattering for symbolic potentials of order zero and microlocal propagation near radial points (2005) (9)
- Resolution of smooth group actions (2010) (9)
- Adiabatic Limit, Heat Kernel and Analytic Torsion (2012) (9)
- Functional Analysis Lecture notes for 18.102 (2010) (8)
- Resolution of the canonical fiber metrics for a Lefschetz fibration (2015) (8)
- Dirac Operators (2020) (8)
- Geometric optics and the bottom of the spectrum (1997) (8)
- Hypoelliptic operators with characteristic variety of codimension two and the wave equation (1980) (8)
- Periodicity and the Determinant Bundle (2006) (8)
- A remark on distributions and the de Rham theorem (2011) (7)
- Singularities and the wave equation on conic spaces (2000) (7)
- RELATIVE CHERN CHARACTER, BOUNDARIES AND INDEX FORMULAS (2008) (7)
- Semi-linear diffraction of conormal waves (1996) (7)
- The Cauchy problem with polynomial growth conditions for partial differential operators with constant coefficients (1975) (7)
- Differential Boundary Value Problems of Principal Type (1979) (7)
- Periodic solutions of certain nonlinear autonomous wave equations (1975) (6)
- Pseudodifferential operators, corners and singular limits : plenary address, International Congress of Mathematicians, Kyoto, Japan, August, 1990 (1990) (6)
- Some spectrally isolated convex planar regions. (1982) (6)
- SCATTERING THEORY FOR STRICTLY PSEUDOCONVEX DOMAINS (1996) (5)
- Eta forms and the odd pseudodifferential families index (2009) (5)
- Equivariant cohomology and resolution (2009) (5)
- TRANSFORMATION METHODS FOR BOUNDARY VALUE PROBLEMS (1981) (5)
- Loop-fusion cohomology and transgression (2013) (4)
- Interaction of progressing waves through a nonlinear potential (1984) (4)
- Non-linear interaction of a cusp and a plane (1995) (4)
- Microlocal analysis and nonlinear waves (1991) (4)
- RELATIVE CHERN CHARACTER , BOUNDARIES AND INDEX FORMULÆ (2008) (3)
- Geometry of pseudodifferential algebra bundles and Fourier integral operators (2012) (3)
- Conormality, cusps and non-linear interaction (1991) (3)
- Equivariant K-theory and Resolution I: Abelian Actions (2018) (3)
- Generalized Robinson-Schensted Algorithms (2009) (2)
- Behaviour at the boundary of the complex Monge-Ampère equation (1981) (2)
- Conormal rings and semilinear wave equations (1986) (2)
- CORNERS AND SINGULAR LIMITS (2007) (2)
- Boundaries, Eta Invariant and the Determinant Bundle (2006) (2)
- Delocalized equivariant cohomology and resolution (2010) (1)
- Analysis on Loop Spaces (2021) (1)
- C ∗ -ALGEBRAS OF B-PSEUDODIFFERENTIAL OPERATORS AND AN R k -EQUIVARIANT INDEX THEOREM (1996) (1)
- Equivariant K-theory and Resolution II: Non-Abelian actions (2020) (1)
- 18.103 Fourier Analysis - Theory and Applications, Spring 2004 (2004) (0)
- D G ] 1 4 Se p 20 07 Boundaries , eta invariant and the determinant bundle (2008) (0)
- NOTES FOR 18.156 SPRING 2020 (2020) (0)
- Bigerbes (2019) (0)
- RICHARD MELROSE Tuesday and Thursdays, 1-2:30 in Room 4-102. The book is Adams and Guillemin (2004) (0)
- Examples of non-discreteness for the interaction geometry of semilinear progressing waves in two space dimensions (1988) (0)
- LECTURE NOTES FOR 18.155, FALL 1997 (1997) (0)
- 18.103, SPRING 2004; SUPPLEMENTAL NOTES (2004) (0)
- Contact Degree (1998) (0)
- Contact Degree (1998) (0)
- DIRAC OPERATORS AND BOUNDARIES, 18.158, FALL 2003 (2003) (0)
- Scattering matrix for asymptotically euclidean manifolds (1994) (0)
- I.M: Fractional analytic index (0)
- 18.100B Analysis I, Fall 2002 (2002) (0)
- THE PROBLEMS FOR THE SECOND TEST FOR 18.102 BRIEF SOLUTIONS (2015) (0)
- Elliptic regularity and Monopoles (2007) (0)
- RESOLUTION OF SMOOTH GROUP ACTIONS PIERRE ALBIN AND RICHARD MELROSE (2010) (0)
- Compactification of SL(2) (2018) (0)
- LECTURE NOTES FOR 18.155, FALL 2004 (2002) (0)
- Compactification of semi-simple Lie groups. (2019) (0)
- COHOMOLOGY AND INDEX JOINT WORK WITH PIERRE ALBIN FOR WERNER MÜLLER ’ S 60 TH BIRTHDAY (2010) (0)
- Adiabatic Limit with Isolated Degenerate Fibres (2013) (0)
- 2. Cone Support and Wavefront Set (0)
- PROBLEM SET 1 FOR 18.102, SPRING 2020 BRIEF SOLUTIONS (2020) (0)
- Resolution of Smooth Group Actions Accessed Terms of Use Detailed Terms Resolution of Smooth Group Actions (2010) (0)
- 18.155 Differential Analysis, Fall 2002 (2002) (0)
- 18.156 – GRADUATE ANALYSIS ELLIPTIC REGULARITY AND SCATTERING (2008) (0)
- - 1-PROGRESSING WAVE SOLUTIONS TO NONLINEAR HYPERBOLIC CAUCHY PROBLEMS (2018) (0)
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