
Geometry of Pseudodifferential algebra bundles
and Fourier Integral Operators
with Mathai Varghese
23 October, 2012.
SmoothAzumaya.pdf

Generalized blowup of corners and fiber products
with Chris Kottke
16 October, 2012.
Resolve.pdf

Delocalized equivariant cohomology and resolution
with Pierre Albin
26 December, 2010.
AlbinMelroseDeLoRe.dvi
AlbinMelroseDeLoRe.ps
(postscript file)
AlbinMelroseDeLoRe.pdf
(acrobat file)

Resolution of smooth group actions
with Pierre Albin
arXiv:
9 August, 2010.
ResGrp.dvi
ResGrp.ps
(postscript file)
ResGrp.pdf
(acrobat file)

Equivariant cohomology and resolution
with Pierre Albin
arXiv:0905.3211
This paper has been divided into two and extensively rewritten as the two papers above.
eqcores.dvi
eqcores.ps
(postscript file)
eqcores.pdf
(acrobat file)

Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary
with Pierre Albin
arXiv:0905.0453
6 May, 2009.
fresmb.dvi
fresmb.ps
(postscript file)
fresmb.pdf
(acrobat file)

Eta forms and the odd pseudodifferential families index
with Frédéric Rochon
arXiv:0905.0150
6 May, 2009.
efatopi.dvi
efatopi.ps
(postscript file)
efatopi.pdf
(acrobat file)

Diffraction of singularities for the wave equation on manifolds with
corners
with András Vasy and Jared Wunsch
arXiv:0811.2228
18 March, 2009.
corners.dvi
corners.ps
(postscript file)
corners.pdf
(acrobat file)

The index of projective families of elliptic operators: the decomposable case
with Varghese Mathai and Is Singer
arXiv:0809.0028
Version 1.1I, 17 March, 2009.
Decomposable.dvi
Decomposable.ps
(postscript file)
Decomposable.pdf
(acrobat file)

Asymptotics of solutions of the wave equation on de SitterSchwarzschild
space
with Antônio sà Barreto and András Vasy
arXiv:0811.2229
17 March, 2009.
dssch.dvi
dssch.ps
(postscript file)
dssch.pdf
(acrobat file)

Scattering configuration spaces
with Michael Singer
arXiv:0808.2022
Initial version, 15 August, 2008.
ScatProd.dvi
ScatProd.ps
(postscript file)
ScatProd.pdf
(acrobat file)
Relative Chern character, boundaries and index formulae
with Pierre Albin
arXiv:0808.0183
Initial version, 1 August, 2008.
rccbif.dvi
rccbif.ps
(postscript file)
rccbif.pdf
(acrobat file)

Generalized backscattering and the LaxPhillips transform
with Gunther Uhlmann
Arxiv: math.AP/0712.4236
Initial version of 27 December, 2007.
Small corrections, 2 January December, 2008.
Further small corrections, 3 January December, 2008.
(But really a chapter from an old book manuscript!)
BackScat.dvi
BackScat.ps
(postscript file)
BackScat.pdf
(acrobat file)

Boundaries, eta invariant and the determinant bundle
with Frédéric Rochon
ArXiv:math/0607480
beidb.dvi
beidb.ps
(postscript file)
beidb.pdf
(acrobat file)

Fredholm realizations of elliptic symbols on manifolds with boundary
with Pierre Albin
Arxiv: math/0607154
fresmb0sc.dvi
fresmb0sc.ps
(postscript file)
fresmb0sc.pdf
(acrobat file)

Propagation of singularities for the wave equation on edge manifolds
with András Vasy and Jared Wunsch
Arxiv: math.AP/0612750
Initial version of 24 December, 2006.
New version, 5th November, 2007:
Edges.dvi
Edges.ps
(postscript file)
Edges.pdf
(acrobat file)

Equivariant and fractional index of projective elliptic operators
with Varghese Mathai and Is Singer
Arxiv: math.DG/0611819
Initial version of 27 November, 2006.
New version, 11 May, 2007:
JDG version, 28 March, 2008:
Fractequivindex.dvi
Fractequivindex.ps
(postscript file)
Fractequivindex.pdf or
JDG version
(acrobat file)

Periodicity and the determinant bundle
with Frédéric Rochon
Revised version of 29 November, 2006.
Initial version of 15 June, 2006.
perdet.dvi
perdet.ps
(postscript file)
perdet.pdf
(acrobat file)

Index in Ktheory for Families of fibred cusp operators
with Frédéric Rochon
Initial version of 4 July, 2005.
New version (on Arxiv as 0507590)
Revised version of 4 March 2006 (to appear in K Theory).
faficu.dvi
faficu.ps
(postscript file)
faficu.pdf
(acrobat file)

Star products and local line bundles
Initial version of 11 July, 2004.
Current version, 5 October, 2004. Accepted for publication in l'Annales de l'Institut Fourier, special volume for Louis Boutet de Monvel
spallb.dvi
spallb.ps
(postscript file)
spallb.pdf
(acrobat file)

Fractional analytic index
with V. Mathai and I.M. Singer
Version of 20 Feb, 2004  essentially as on Arxiv:DG/0402329; relation to CheegerSimons added.
[Version of 17 Feb, 2004].
Originally posted 3 Feb, 2004
mms3.dvi
mms3.ps
(postscript file)
mms3.pdf
(acrobat file)

The inverse spectral problem for planar domains
Lectures at ANU that I had forgotten to put on the web!
anulec.dvi
(You will need these twelve eps files too if you want the figures)
anulec.ps
(postscript file)
anulec.pdf
(acrobat file)

Families index for pseudodifferential operators on manifolds with boundary
with Frédéric Rochon
Version of 25 May, 2003
fipomb.dvi
fipomb.ps
(postscript file)
fipomb.pdf
(acrobat file)

The index of projective families of elliptic operators
with V. Mathai and I.M. Singer
Originally posted 31 May, 2002; Version of 1 June, 2002
mms2001.dvi
mms2001.ps
(postscript file)
mms2001.pdf
(acrobat file)

Propagation of singularities for the wave equation on conic manifolds
with Jared Wunsch
Version of 22 November (original 29 October), 2001
melwun1.dvi
melwun1.ps
(postscript file)
melwun1.pdf
(acrobat file)

Spectral and scattering theory for symbolic potentials of order zero, I
with Andrew Hassell and András Vasy
Version of 13 December, 2001
HMV1.dvi
HMV1.ps
(postscript file)
HMV1.pdf
(acrobat file)

A remark on distributions and the de Rham theorem
If you have seen this sort of proof somewhere, please let me know!
Original posted November 17, 1999
Second version January 22, 2000: Some typos corrected (thanks to Jukka Liukkonen)
New Version 11 May, 2011: Error in the proof of Lemma 4 noticed by Yi Lin corrected
deRham.dvi
deRham.ps
(postscript file)
deRham.pdf
(acrobat file)

Contact degree and the index of Fourier integral operators
Joint work with C. Epstein
To appear in Mathematics Research Letters
Version from proofs, May 27, 1998
(First version 2nd February 1998)
cdifio.dvi
cdifio.ps
(postscript file)
cdifio.pdf
(acrobat file)

Contact degree
Superceded by the paper above.
Joint work with C. Epstein
This is a short note describing an extended form of Weinstein's question on the index of Fourier integral operators in terms of the notion of the `degree' of a contact diffeomorphism
Version of January 8, 1998.
(postscript file)
ConDeg.pdf
(acrobat file)

Pseudodifferential operators on manifolds with fibred boundaries
Joint work with Rafe Mazzeo
To appear in the special volume of the Asian Journal of Mathematics celebrating the 70th birthday of Professor Mikio Sato.
Version of 10th of March, 1999 (another typo squashed).
poomwfb.dvi
(dvi)
double.eps
(figure)
Triple.eps(figure)
poomwfb.ps
(postscript)
poomwfb.pdf
(acrobat)

Homology and the Heisenberg algebra
Joint work with C. Epstein and G. Mendoza
(not the Eisenberg algebra as originally advertised!)
Short write up for a seminar at Ecole Poytechnique, may 20, 1997
Version of July 7, 1997.
HoHe.dvi
(amslatex dvi file with encapsulated postscript inserts)
HoHe.ps
(postscript file)

Geometric optics and the bottom of the spectrum
Written up (and extended) version of a talk at the meeting
`Geometrical optics and related topics'
at Cortona, September 1996.
Version of November 8, 1996.
Abstract
Cortona.dvi
(amstex dvi file)
Cortona.ps
(postscript file)

Ktheory of $C^*$algebras of bpseudodifferential operators
(Old title: Ktheory of bpseudodifferential operators
and an {$\RR^k$}equivariant index theorem)
Preprint, October 18, 1996.
Abstract
(Revised version of September 10, 1997)
ktobpo.ps (In postscript format)
ktobpo.pdf (In acrobat format)
ktobpo.dvi (In dvi format)

Homology of pseudodifferential operators I.
Manifolds with boundary
Preprint, May 29, 1996.
Abstract
hopo1.ps
(postscript file)

Fibrations, compactifications and
algebras of pseudodifferential operators
Published in: ``Partial Differential Equations and Mathematical Physics. The DanishSwedish Analysis Seminar, 1995''
Editors, Lars H\"ormander and Anders Melin.
Birkhauser, 1996.
Pages 246261.
Abstract
fcaaopo.ps
(postscript file)

The eta invariant of pseudodifferential operators
Published in: Math. Res. Letters, Vol 2, No. 5, 1995, pp 541561
Abstract
teiafp.ps
(postscript file)

Scattering metrics and geodesic flow at infinity
with Maciej Zworski
Published in: Invent. Math., Vol 124 (1996), pp 389436.
Abstract
[Diagrams are currently missing from smagai]
smagai.ps
(postscript file)
smagai.pdf
(acrobat file)

Signature theorem for manifolds with corners
of codimension 2
with Andrew Hassell and Rafe Mazzeo
To appear in Topology
(revised September 10, 1996)
Abstract
stmwc.ps
(postscript file)
stmwc.pdf
(Adobe portable document format file)

Spectral and scattering theory for the Laplacian
on asymptotically Euclidian spaces
Published in: "Spectral and scattering theory",
Edited by M. Ikawa, 1994, Marcel Dekker.
Introduction
As published:
sslaes.ps
(postscript file)
Corrected , (Jan 15, 1997):
sslaes1.dvi (dvi file, needs lamstex fonts)
sslaes1.ps (postscript file)
sslaes1.pdf (acrobat file)

An index theorem for families of Dirac operators
on odddimensional manifolds with boundary
with Paolo Piazza
J. Diff. Geom. 46 (1997) 287334
Abstract
ofapsi.ps
(postscript file)

Families of Dirac operators, boundaries
and the bcalculus
with Paolo Piazza
J. Diff. Geom. 46 (1997) 99180
Abstract
fdobbc.ps
(postscript file)

Semilinear Diffraction of Conormal Waves
with Antonio Sa Barreto and Maciej Zworski
Asterisque.
sldall.ps

Pseudodifferential operators, corners and singular limits
talk at ICM in Kyoto, 1990
kyoto.dvi
kyoto.ps (postscript)
kyoto.pdf (acrobat)

Isospectral sets of drumheads are compact in C^{∞}
Unpublished preprint from MSRI, 04883, 1983
isospectral.pdf (acrobat file)
isospectral.dvi(dvi file)
isosp.pdf (acrobat  scan of the preprint)

Elliptic operators of totally characteristic type
with Gerardo Mendoza: Unpublished preprint from MSRI, 04783, 1983
belliptic1983.pdf (acrobat file  needs proofreading!)
belliptic1983.dvi(dvi file  needs proofreading!)
1983MelroseMendoza.pdf (acrobat  scan of the preprint)