
Academic Appointments
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Professor, Mathematics
Administrative Appointments
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Professor, Department of Mathematics, Stanford University (2008 - Present)
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Associate Professor, Department of Mathematics, Stanford University (2005 - 2008)
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Visiting Associate Professor, Department of Mathematics, Northwestern University (2004 - 2005)
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Associate Professor, Department of Mathematics, Massachusetts Institute of Technology (2003 - 2006)
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Enseignant invité, Département de Mathématiques, Université de Nantes (2002 - 2002)
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Local organizer, Programme in Scattering Theory, Erwin Schrödinger Institute, Vienna, Austria (2001 - 2001)
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Assistant Professor, Department of Mathematics, Massachusetts Institute of Technology (1999 - 2003)
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Morrey Assistant Professor, Department of Mathematics, University of California, Berkeley (1997 - 2000)
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Teaching Assistant, Department of Mathematics, Massachusetts Institute of Technology (1993 - 1996)
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Alfred P. Sloan Research Fellowship, Alfred P. Sloan Foundation (2002 - 2004)
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Alfred P. Sloan Doctoral Dissertation Fellowship, Alfred P. Sloan Foundation (1996 - 1997)
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Clay Research Fellowship, Clay Mathematics Institute (2004 - 2006)
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Chambers Fellowship, Stanford University (2008 - 2009)
Honors & Awards
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Invited speaker for the Partial Differential Equations section, International Congress of Mathematicians, Seoul (2014)
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Jennifer C. Johnson prize for the best research paper, Department of Mathematics of Massachusetts Institute of Technology (1997)
Boards, Advisory Committees, Professional Organizations
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Co-organizer, Programme on the ‘Modern Theory of Wave Equations’, Erwin Schrödinger Institute, Vienna, Austria
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Co-organizer, ‘A conference on Inverse Problems in honor of Gunther Uhlmann’, University of California, Irvine (2012 - 2012)
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Co-organizer, conference ‘Microlocal methods in spectral and scattering theory’, Northwestern University (2011 - 2011)
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Co-organizer, conference ‘Microlocal methods in mathematical physics and global analysis’, Tübingen, Germany (2011 - 2011)
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Co-organizer, conference ‘From wave propagation to K-theory’, Stanford University (2008 - 2008)
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Co-organizer, semester-long Program on Analysis of Singular Spaces, Mathematical Sciences Research Institute, Berkeley, CA (2008 - 2008)
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Co-organizer, conference on Spectral Theory and Global Analysis, University of Oldenburg, Germany (2006 - 2006)
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Co-organizer, Scattering Theory and Singular Spaces, Northwestern University (2005 - 2005)
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Co-organizer, conference on Scattering Theory and Singular Spaces, Northwestern University (2005 - 2005)
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Co-organizer, Geometric Analysis: a conference in Honor of Richard Melrose, Massachusetts Insitute of Technology (2002 - 2002)
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Local organizer, semester-long Programme in Scattering Theory, Erwin Schrödinger Institute, Vienna, Austria (2001 - 2001)
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Member, Graduate Admissions Committee, Stanford University, Department of Mathematics (2013)
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Member, Natural Sciences Curriculum Review Committee, Stanford University, School of Humanities and Sciences (2012 - 2013)
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Member, Appointments Committee, Stanford University, Department of Mathematics (2011 - 2013)
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Member, Director of Graduate Studies, Stanford University, Department of Mathematics (2007 - 2010)
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Member, Graduate Admissions Committee, Stanford University, Department of Mathematics (2006 - 2006)
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Member, Graduate Admissions Committee, Stanford University, Department of Mathematics (2007 - 2007)
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Editor, Analysis & PDE (journal) (2007 - Present)
Professional Education
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Ph.D., Massachusetts Institute of Technology, Mathematics (1997)
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M.S., Stanford University, Mathematics (1993)
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B.S., Stanford University, Physics (1993)
2020-21 Courses
- Elementary Functional Analysis
MATH 175 (Aut) - Proofs and Modern Mathematics
MATH 56 (Aut) - Real Analysis
MATH 205B (Win) -
Independent Studies (3)
- Advanced Reading and Research
MATH 360 (Aut, Win, Spr, Sum) - Independent Research and Study
PHYSICS 190 (Win, Spr, Sum) - Senior Honors Thesis
MATH 197 (Aut, Win, Spr)
- Advanced Reading and Research
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Prior Year Courses
2019-20 Courses
- Elementary Functional Analysis
MATH 175 (Win) - Real Analysis
MATH 205B (Win) - Real Analysis
MATH 205C (Spr)
2018-19 Courses
- Ordinary Differential Equations with Linear Algebra
MATH 53 (Win) - Partial Differential Equations of Applied Mathematics
CME 303, MATH 220 (Aut) - Proofs and Modern Mathematics
MATH 83N (Aut)
- Elementary Functional Analysis
Stanford Advisees
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Postdoctoral Faculty Sponsor
Oliver Lindblad Petersen -
Doctoral Dissertation Advisor (AC)
Qiuye Jia, Joey Zou -
Doctoral Dissertation Co-Advisor (AC)
Rahul Sarkar
All Publications
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Morawetz estimates for the wave equation at low frequency
MATHEMATISCHE ANNALEN
2013; 355 (4): 1221-1254
View details for DOI 10.1007/s00208-012-0817-x
View details for Web of Science ID 000316870300002
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MULTISCALE DISCRETE APPROXIMATIONS OF FOURIER INTEGRAL OPERATORS ASSOCIATED WITH CANONICAL TRANSFORMATIONS AND CAUSTICS
MULTISCALE MODELING & SIMULATION
2013; 11 (2): 566-585
View details for DOI 10.1137/120889642
View details for Web of Science ID 000321038600007
- Diffraction of singularities for the wave equation on manifolds with corners Astérisque 2013; 351: 136
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DIFFRACTION OF SINGULARITIES FOR THE WAVE EQUATION ON MANIFOLDS WITH CORNERS
ASTERISQUE
2013: 1-?
View details for Web of Science ID 000326612800001
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SEMICLASSICAL RESOLVENT ESTIMATES AT TRAPPED SETS
ANNALES DE L INSTITUT FOURIER
2012; 62 (6): 2379-2384
View details for Web of Science ID 000316032000012
- Spectral theory for the Weil-Petersson Laplacian on the Riemann moduli space To appear in Commentarii Mathematici Helvetici 2012: 26
- Microlocal analysis of asymptotically hyperbolic spaces and high energy resolvent estimates In Inverse problems and applications edited by Uhlmann, G. Cambridge University Press, MSRI Publications. 2012: 31
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Gluing Semiclassical Resolvent Estimates via Propagation of Singularities
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
2012: 5409-5443
View details for DOI 10.1093/imrn/rnr255
View details for Web of Science ID 000311666800004
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PROPAGATION THROUGH TRAPPED SETS AND SEMICLASSICAL RESOLVENT ESTIMATES
ANNALES DE L INSTITUT FOURIER
2012; 62 (6): 2347-2377
View details for Web of Science ID 000316032000011
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THE WAVE EQUATION ON ASYMPTOTICALLY ANTI DE SITTER SPACES
ANALYSIS & PDE
2012; 5 (1): 81-144
View details for DOI 10.2140/apde.2012.5.81
View details for Web of Science ID 000306905600003
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Positive commutators at the bottom of the spectrum
JOURNAL OF FUNCTIONAL ANALYSIS
2010; 259 (2): 503-523
View details for DOI 10.1016/j.jfa.2010.04.012
View details for Web of Science ID 000277528000008
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The wave equation on asymptotically de Sitter-like spaces
ADVANCES IN MATHEMATICS
2010; 223 (1): 49-97
View details for DOI 10.1016/j.aim.2009.07.005
View details for Web of Science ID 000271699900003
- Diffraction at corners for the wave equation on differential forms Comm. in PDEs 2010; 35: 1236-1275
- Gluing semiclassical resolvent estimates, or the importance of being microlocal Oberwolfach Reports 2010; 7 (2): 1648-1651
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SEMICLASSICAL SECOND MICROLOCAL PROPAGATION OF REGULARITY AND INTEGRABLE SYSTEMS
JOURNAL D ANALYSE MATHEMATIQUE
2009; 108: 119-157
View details for Web of Science ID 000283485800005
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Propagation of singularities for the wave equation on manifolds with corners
ANNALS OF MATHEMATICS
2008; 168 (3): 749-812
View details for Web of Science ID 000263764100002
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DIFFRACTION BY EDGES
International Conference on Inversese Quantum Scattering Theory
WORLD SCIENTIFIC PUBL CO PTE LTD. 2008: 2287–2328
View details for Web of Science ID 000259926500014
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Propagation of singularities for the wave equation on edge manifolds
DUKE MATHEMATICAL JOURNAL
2008; 144 (1): 109-193
View details for DOI 10.1215/00127094-2008-033
View details for Web of Science ID 000257603700004
- Scattering for symbolic potentials of order zero and microlocal propagation near radial points Analysis & PDE 2008; 1: 127-196
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Scattering theory on SL(3)/SO(3): Connections with quantum 3-body scattering
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
2007; 94: 545-593
View details for DOI 10.1112/plms/pdl004
View details for Web of Science ID 000247283100001
- Geometric optics and the wave equation on manifolds with corners Contemp. Math. 2006; 412: 315-333
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Analytic continuation of the resolvent of the Laplacian on symmetric spaces of noncompact type
JOURNAL OF FUNCTIONAL ANALYSIS
2005; 228 (2): 311-368
View details for DOI 10.1016/j.jfa.2004.10.003
View details for Web of Science ID 000233141400003
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Absence of super-exponentially decaying eigenfunctions on Riemannian manifolds with pinched negative curvature
MATHEMATICAL RESEARCH LETTERS
2005; 12 (5-6): 673-684
View details for Web of Science ID 000234367800005
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Lipschitz domains, domains with corners, and the Hodge Laplacian
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
2005; 30 (10): 1445-1462
View details for DOI 10.1080/03605300500299547
View details for Web of Science ID 000233089500002
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Analytic continuation of the resolvent of the Laplacian on SL(3)/SO(3)
AMERICAN JOURNAL OF MATHEMATICS
2004; 126 (4): 821-844
View details for Web of Science ID 000223184500005
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Inverse scattering with fixed energy for dilation-analytic potentials
INVERSE PROBLEMS
2004; 20 (4): 1349-1354
View details for DOI 10.1088/0266-5611/20/4/020
View details for Web of Science ID 000223542200020
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Complex powers and non-compact manifolds
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
2004; 29 (5-6): 671-705
View details for DOI 10.1081/PDE-120037329
View details for Web of Science ID 000221659800003
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Exponential decay of eigenfunctions in many-body type scattering with second-order perturbations
JOURNAL OF FUNCTIONAL ANALYSIS
2004; 209 (2): 468-492
View details for DOI 10.1016/S0022-1236(03)00106-X
View details for Web of Science ID 000220525300009
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Spectral and scattering theory for symbolic potentials of order zero
ADVANCES IN MATHEMATICS
2004; 181 (1): 1-87
View details for DOI 10.1016/S0001-8708(03)00020-3
View details for Web of Science ID 000187564300001
- Inverse problems in N-body scattering Inverse Problems and Spectral Theory edited by Isozaki, H. 2004
- Geometry and analysis in many-body scattering. Inside-out: Inverse problems Math. Sci. Res. Inst. Publ 2003; 47: 333-379
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Low-energy inverse problems in three-body scattering
INVERSE PROBLEMS
2002; 18 (3): 719-736
View details for Web of Science ID 000176750400014
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Resolvents and Martin boundaries of product spaces
GEOMETRIC AND FUNCTIONAL ANALYSIS
2002; 12 (5): 1018-1079
View details for Web of Science ID 000179562000005
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Smoothness and high energy asymptotics of the spectral shift function in many-body scattering
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
2002; 27 (11-12): 2139-2186
View details for DOI 10.1081/PDE-120016156
View details for Web of Science ID 000179929300002
- Fixed energy inverse problem for exponentially decaying potentials Methods Appl. Anal 2002; 9: 239-248
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Propagation of singularities in many-body scattering in the presence of bound states
JOURNAL OF FUNCTIONAL ANALYSIS
2001; 184 (1): 177-272
View details for Web of Science ID 000170498600005
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Intersecting Legendrians and blow-ups
MATHEMATICAL RESEARCH LETTERS
2001; 8 (4): 413-428
View details for Web of Science ID 000171111000002
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Propagation of singularities in many-body scattering
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
2001; 34 (3): 313-402
View details for Web of Science ID 000169964700001
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The resolvent for Laplace-type operators on asymptotically conic spaces
ANNALES DE L INSTITUT FOURIER
2001; 51 (5): 1299-?
View details for Web of Science ID 000174292900007
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Symbolic functional calculus and N-body resolvent estimates
JOURNAL OF FUNCTIONAL ANALYSIS
2000; 173 (2): 257-283
View details for Web of Science ID 000087445300001
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Semiclassical estimates in asymptotically Euclidean scattering
COMMUNICATIONS IN MATHEMATICAL PHYSICS
2000; 212 (1): 205-217
View details for Web of Science ID 000087859100008
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Propagation of singularities in three-body scattering
ASTERISQUE
2000: III-?
View details for Web of Science ID 000086395100001
- Propagation of singularities in three-body scattering Asterisque 2000; 262
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The spectral projections and the resolvent for scattering metrics
JOURNAL D ANALYSE MATHEMATIQUE
1999; 79: 241-298
View details for Web of Science ID 000086439100009
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Scattering matrices in many-body scattering
COMMUNICATIONS IN MATHEMATICAL PHYSICS
1999; 200 (1): 105-124
View details for Web of Science ID 000078638100006
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Geometric scattering theory for long-range potentials and metrics
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
1998: 285-315
View details for Web of Science ID 000073347900001
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Structure of the resolvent for three-body potentials
DUKE MATHEMATICAL JOURNAL
1997; 90 (2): 379-434
View details for Web of Science ID A1997YG81000003
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Asymptotic behavior of generalized eigenfunctions in N-body scattering
JOURNAL OF FUNCTIONAL ANALYSIS
1997; 148 (1): 170-184
View details for Web of Science ID A1997XP74400007
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Scattering poles for negative potentials
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
1997; 22 (1-2): 185-194
View details for Web of Science ID A1997WL70400009