Plamen Stefanov

Professor of Mathematics, Purdue University

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Publications

Vita    Talks, mini-courses and lecture notes

  1. Boundary determination and local rigidity of analytic metrics in the Lorentzian scattering rigidity problem. [ pdf ]

  2. The Lorentzian scattering rigidity problem and rigidity of stationary  metrics. [ pdf ] [ arXiv:2212.13213 ]

  3. Weakly nonlinear geometric optics for the Westervelt equation and recovery of the nonlinearity (with N. Eptaminitakis), SIAM J. Math. Anal., 56(1): 801-819, 2024. [ pdf ] [ DOI ]

  4. The solid-fluid transmission problem (with N. Eptaminitakis), to appear in Trans. Am. Math. Soc. [ pdf ] [ arXiv:2111.03218 ]

  5. Inverse problems for real principal type operators (with M. Salo, L. Oksanen and G. Uhlmann), Amer. J. Math.   146(1), 161-240, 2024 [ pdf ] [ DOI ] 

  6. Recovery of a general nonlinearity in the semilinear wave equation (with A. Sá Barreto), to appear in Asympt. Anal. [ pdf ] [ arXiv:2107.08513 ]

  7. The Radon transform with finitely many angles, Inverse Probl. 39 105003, 2023. [ pdf ] [ DOI ]

  8. Sampling the X-ray transform on simple surfaces (with F. Monard), SIAM J. Math. Anal., 55(3), 1707-1736, 2023. [ pdf ] [ DOI ]

  9. Sampling linear inverse problems with noise (with Samy Tindel). Asympt. Anal. 132, 331-382, 2023. [ pdf ] [ DOI ]

  10. Inverse Boundary Problem for the Two Photon Absorption Transport Equation (with Y. Zhong), SIAM J. Math. Anal., 54(3), 2753-2767, 2022. [ pdf ] [ DOI ]

  11. Recovery of a cubic non-linearity in the wave equation in the weakly non-linear regime (with A. Sá Barreto), Commun. Math. Phys. 392, 25-53, 2022. [ pdf ] [ DOI ]

  12. The transmission problem in linear isotropic elasticity (with G. Uhlmann and A. Vasy), Pure and Applied Analysis, 3-1, 109-161, 2021. [ pdf ] [ DOI ]

  13. A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold (with M. Bellassoued, M. Choulli, Dos Santos Ferreira and Y. Kian). Ann. Inst. Fourier (Grenoble), 71(6), 2471-2517, 2021. [ pdf ] [ DOI ]

  14. Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge (with G. Uhlmann and A. Vasy). Ann. Math. (2), 194, 1-95, 2021. [ pdf ] [ DOI ]  *** A Nature news article about it and AMS mentioning of it. Discover Magazine ranks it #56 top story of 2017 (the only other math one is #17 there). Also, Scientific American, PBS and AZoMining run stories.  *** Received one of the Frontiers of Science Awards at the International Congress of Basic Science 2023: one of the best three papers in Geometric Analysis in 2018-2023.  

  15. The Light Ray transform on Lorentzian manifolds (with M. Lassas, L. Oksanen and G. Uhlmann), Commun. Math. Phys., 377, 1349-1379, 2020. [ pdf ] [ DOI ]

  16. Semiclassical sampling and discretization of certain linear inverse problems. SIAM J. Math. Anal., 52(6), 5554-5597, 2020. [ pdf ] [ DOI ]

  17. Sharp stability estimate for the geodesic ray transform (with Y. Assylbekov), Inverse Problems, 36(2), 025013, 2020. [ pdf ] [DOI ]

  18. X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds (with R. Graham, C. Guillarmou, and G. Uhlmann). Ann. Inst. Fourier (Grenoble), 69(7), 2857-2919, 2019. [ pdf ] [ DOI ]

  19. Conditionally stable unique continuation and applications to thermoacoustic tomography, Mathematics in Engineering, 1(4): 789–799, 2019. [ pdf ] [ DOI ]

  20. Travel Time Tomography (with G. Uhlmann, A. Vasy and H. Zhou), Acta Mathematica Sinica, English Series. 35(6), 1085-1114, 2019. [ pdf ] [ DOI ]

  21. The inverse problem for the Dirichlet-to-Neumann map on Lorentzian manifolds (with Y. Yang), Analysis PDE, 11, No. 6, 1381-1414, 2018. [ pdf ] [ DOI ]

  22. Inverting the local geodesic X-ray transform on tensors (with G. Uhlmann and A. Vasy), Journal d'Analyse Mathématique, 136(1), 151-208, 2018. [ pdf ] [ DOI ]

  23. The attenuated geodesic X-ray transform (with S. Holman and F. Monard), Inverse Problems 34, 064003, 2018. [ pdf ] [ DOI ]

  24. Local recovery of the compressional and shear speeds from the hyperbolic DN map (with G. Uhlmann and A. Vasy), Inverse Problems 34 014003, 2018. [ pdf ] [ DOI ]

  25. On the inverse problem of finding cosmic strings and other topological defects (with M. Lassas, L. Oksanen and G. Uhlmann), Comm. Math. Phys. 357(2), 569-595, 2018.  [ pdf ] [ DOI ]

  26. Thermo and Photoacoustic Tomography with variable speed and planar detectors (with Y. Yang), SIAM J. Math. Anal., 49(1), 297-310, 2017. [ pdf ] [ DOI ]

  27. Multiwave tomography with reflectors: Landweber's iteration (with Y. Yang), Inverse Problems and Imaging, 11(2), 373-401, 2017. [ pdf ] [ DOI ]

  28. Support theorems for the Light Ray transform on analytic Lorentzian manifolds, Proc. Amer. Math. Soc. 145(3), 1259-1274, 2017. [ pdf ] [ DOI ]

  29. Boundary rigidity with partial data (with G. Uhlmann and A. Vasy), J. Amer. Math. Soc. 29, 299-332, 2016. [ pdf ] [ DOI ]

  30. On the stable recovery of a metric from the hyperbolic DN map with incomplete data (with G. Uhlmann and A. Vasy), Inverse Problems and Imaging, 1141-1147, 10(4), 2016. [ pdf  ] [ DOI ]

  31. Microlocal Analysis Methods. In the Encyclopedia of Applied and Computational Mathematics, Springer, 914-920, 2015. [ pdf ] [ DOI ]

  32. Multiwave tomography in a closed domain: averaged sharp time reversal (with Y. Yang), Inverse Problems, 31, 065007, 2015. [ pdf ] [ DOI ]

  33. Modulated Luminescence Tomography (with W. Cong and Ge Wang), Inverse Problems and Imaging, 9(2), 551-578, 2015. [ pdf ] [ DOI ]

  34. The geodesic ray transform on Riemannian surfaces with conjugate points (with F. Monard and G. Uhlmann), Commun. Math. Phys. 337(3), 1491-1513, 2015. [ pdf ] [ DOI ]

  35. X-ray micromodulated luminescence tomography in dual-cone geometry (with W. Cong, Z. Pan, R. Filkins, A. Srivastava, N. Ishaque and Ge Wang). J. Biomed. Optics 19(7), 076002, 2014. [ pdf ] [ DOI ]

  36. Weyl asymptotics of the transmission eigenvalues for a constant index of refraction (with Ha Pham), Inverse Problems and Imaging, 8(3), 795-810, 2014. [ pdf ] [ DOI ]

  37. Adjoint state method for recovery both the attenuation and the source in the attenuated X-ray transform (with S. Luo and J. Qian), SIAM J. Imaging Sceinces, 7(2), 696-715, 2014. [ pdf ] [ DOI ]

  38. The Identification Problem for the attenuated X-ray transform, Amer. J. Math. 136(5): 1215-1247, 2014. [ pdf ] [ DOI ]

  39. Stability of Coupled-Physics Inverse Problems with one internal measurement (with C. Montalto). Inverse Problems, 12:125004, 2013. [ pdf ] [ DOI ]

  40. Instability of the linearized problem in multiwave tomography of recovery both the source and the speed (with G. Uhlmann). Inverse Problems and Imaging, 7(4):1367-1377, 2013. [ pdf ][ DOI ]

  41. Recovery of a source term or a speed with one measurement and applications (with G. Uhlmann). Trans. Amer. Math. Soc., 365(11):5737-5758, 2013. [ pdf ] [ DOI ]

  42. Is a curved flight path in SAR better than a straight one? (with G. Uhlmann) SIAM J. Appl. Math., 73(4):1596-1612, 2013. [ pdf ] [ DOI ]

  43. Stability for the multi-dimensional Borg-Levinson theorem with partial spectral data (with M. Choulli). Comm. Partial Differential Equations, 38(3):455-476, 2013. [ pdf ] [ DOI ]

  44. The geodesic X-ray transform with fold caustics (with G. Uhlmann). Anal. PDE, 5(2):219-260, 2012. [ pdf ] [ DOI ]

  45. Multi-wave methods via ultrasound (with G. Uhlmann), Inside Out II, MSRI publications, 60:271-324, 2012. [ pdf ] [ DOI ]

  46. Stability of the gauge equivalent classes in inverse stationary transport in refractive media (with S. McDowall and A. Tamasan). In Tomography and inverse transport theory, volume 559 of Contemp. Math., pages 85-100. Amer. Math. Soc., Providence, RI, 2011. [ pdf ] [ DOI ]

  47. An efficient Neumann series-based algorithm for thermoacoustic and photoacoustic tomography with variable sound speed (with J. Qian, G. Uhlmann and H. Zhao). SIAM J. Imaging Sci., 4(3):850-883, 2011. [ pdf ][ DOI ]

  48. Thermoacoustic tomography arising in brain imaging (with G. Uhlmann). Inverse Problems, 27(4):045004, 26, 2011. [ pdf ] [ DOI ]

  49. Gauge equivalence in stationary radiative transport through media with varying index of refraction (with S. McDowall and A. Tamasan). Inverse Probl. Imaging, 4(1):151-167, 2010. [ pdf ] [ DOI ]

  50. The weighted Doppler transform (with S. Holman). Inverse Probl. Imaging, 4(1):111-130, 2010. [ pdf ] [ DOI ]

  51. Stability of the gauge equivalent classes in inverse stationary transport (with S. McDowall and A. Tamasan). Inverse Problems, 26(2):025006, 19, 2010. [ pdf ] [ DOI ]

  52. A support theorem for the geodesic ray transform of symmetric tensor fields (with V. Krishnan). Inverse Probl. Imaging, 3(3):453-464, 2009. [ pdf ] [ DOI ]

  53. Local lens rigidity with incomplete data for a class of non-simple Riemannian manifolds (with G. Uhlmann). J. Differential Geom., 82(2):383-409, 2009. [ pdf ] [ DOI ]

  54. Thermoacoustic tomography with variable sound speed (with G. Uhlmann). Inverse Problems, 25(7):075011, 16, 2009. [ pdf ] [ DOI ]

  55. Linearizing non-linear inverse problems and an application to inverse backscattering (with G. Uhlmann). J. Funct. Anal., 256(9):2842-2866, 2009. [ pdf ] [ DOI ]

  56. Uniqueness and non-uniqueness in inverse radiative transfer (with A. Tamasan). Proc. Amer. Math. Soc., 137(7):2335-2344, 2009. [ pdf ] [ DOI ]

  57. Boundary and lens rigidity, tensor tomography and analytic microlocal analysis (with G. Uhlmann). In Algebraic analysis of differential equations from microlocal analysis to exponential asymptotics, pp. 275-293. Springer, Tokyo, 2008. [ pdf ] [ DOI ]

  58. An inverse source problem in optical molecular imaging (with G. Uhlmann). Anal. PDE, 1(1):115-126, 2008. [ pdf ] [ DOI ]

  59. A sharp stability estimate in tensor tomography. J. of Physics: Conference Series, 124:012007, 2008. [ pdf ]

  60. Microlocal approach to tensor tomography and boundary and lens rigidity. Serdica Math. J., 34(1):67-112, 2008. [ pdf ]

  61. Integral geometry on tensor fields on a class of non-simple Riemannian manifolds (with G. Uhlmann). Amer. J. Math., 130(1):239-268, 2008. [ pdf ] [ DOI ]

  62. The X-ray transform for a generic family of curves and weights (with B. Frigyik and G. Uhlmann). J. Geom. Anal., 18(1):89-108, 2008. [ pdf ] [ DOI ]

  63. The boundary rigidity problem in the presence of a magnetic field (with N. Dairbekov, G. Paternain, and G. Uhlmann). Adv. Math., 216(2):535-609, 2007. [ pdf ] [ DOI ]

  64. Sharp upper bounds on the number of the scattering poles. J. Funct. Anal., 231(1):111-142, 2006. [ pdf ] [ DOI ]

  65. Approximating resonances with the complex absorbing potential method. Comm. Partial Differential Equations, 30(10-12):1843-1862, 2005. [ pdf ] [ DOI ]

  66. Boundary rigidity and stability for generic simple metrics (with G. Uhlmann). J. Amer. Math. Soc., 18(4):975-1003, 2005. [ pdf ] [ DOI ]

  67. Recent progress on the boundary rigidity problem (with G. Uhlmann). Electron. Res. Announc. Amer. Math. Soc., 11:64-70, 2005. [ pdf ] [ DOI ]

  68. Stable determination of generic simple metrics from the hyperbolic Dirichlet-to-Neumann map (with G. Uhlmann). Int. Math. Res. Not., (17):1047-1061, 2005. [ pdf ] [ DOI ]

  69. Stability estimates for the X-ray transform of tensor fields and boundary rigidity (with G. Uhlmann). Duke Math. J., 123(3):445-467, 2004. [ pdf ] [ DOI ]

  70. Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering (with G. Uhlmann). Proc. Amer. Math. Soc., 132(5):1351-1354, 2004. [ pdf ] [ DOI ]

  71. Inverse problems in transport theory. In Inside out: inverse problems and applications, volume 47 of Math. Sci. Res. Inst. Publ., pages 111-131. Cambridge Univ. Press, Cambridge, 2003. [ pdf ] [ http ]

  72. Resonance expansions of propagators in the presence of potential barriers (with S. Nakamura and M. Zworski). J. Funct. Anal., 205(1):180-205, 2003. [ pdf ] [ DOI ]

  73. Optical tomography in two dimensions (with G. Uhlmann). Methods Appl. Anal. 10(1):1-9, 2003. [ pdf ] [ DOI ]

  74. Sharp upper bounds on the number of resonances near the real axis for trapping systems. Amer. J. Math., 125(1):183-224, 2003. [ pdf ] [ http ]

  75. Estimates on the residue of the scattering amplitude. Asymptot. Anal., 32(3-4):317-333, 2002. [ pdf ]

  76. Weyl type upper bounds on the number of resonances near the real axis for trapped systems. In Journées “Équations aux Dérivées Partielles” (Plestin-les-Grèves, 2001), pages Exp. No. XIII, 16. Univ. Nantes, Nantes, 2001. [ pdf ]

  77. Resonance expansions and Rayleigh waves. Math. Res. Lett., 8(1-2):107-124, 2001. [ pdf ] [ DOI ]

  78. Lower bounds of the number of the Rayleigh resonances for arbitrary body. Indiana Univ. Math. J., 49(1):405-426, 2000. [ pdf ] [ DOI ]

  79. Resonances near the real axis imply existence of quasimodes. C. R. Acad. Sci. Paris Sér. I Math., 330(2):105-108, 2000. [ pdf ] [ DOI ]

  80. Quasimodes and resonances: sharp lower bounds. Duke Math. J., 99(1):75-92, 1999. [ pdf ] [ DOI ]

  81. An inverse boundary value problem for the stationary transport equation (with M. Choulli). Osaka J. Math., 36(1):87-104, 1999. [ http ] [ pdf ]

  82. Rigidity for metrics with the same lengths of geodesics (with G. Uhlmann). Math. Res. Lett., 5(1-2):83-96, 1998. [ pdf ] [ DOI ]

  83. Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media (with G. Uhlmann). J. Funct. Anal., 154(2):330-358, 1998. [ DOI ]

  84. Scattering theory with two L1 spaces: application to transport equations with obstacles (with M. Mokhtar-Kharroubi and M. Chabi). Ann. Fac. Sci. Toulouse Math. (6), 6(3):511-523, 1997. [ http ]

  85. Inverse backscattering for the acoustic equation (with G. Uhlmann). SIAM J. Math. Anal., 28(5):1191-1204, 1997. [ DOI ]

  86. Reconstruction of the coefficients of the stationary transport equation from boundary measurements (with M. Choulli). Inverse Problems, 12(5):L19-L23, 1996. [ DOI ]

  87. Inverse scattering and inverse boundary value problems for the linear Boltzmann equation (with M. Choulli). Comm. Partial Differential Equations, 21(5-6):763-785, 1996. [ DOI ]

  88. Neumann resonances in linear elasticity for an arbitrary body (with G. Vodev). Comm. Math. Phys, 176(3):645-659, 1996. [ http ]

  89. Distribution of resonances for the Neumann problem in linear elasticity outside a strictly convex body (with G. Vodev). Duke Math. J., 78(3):677-714, 1995. [ DOI ]

  90. Scattering inverse pour l'équation du transport et relations entre les opérateurs de scattering et d'albédo (with M. Choulli). C. R. Acad. Sci. Paris Sér. I Math., 320(8):947-952, 1995.

  91. Distribution des résonances pour le système de l'élasticité (with G. Vodev). In Séminaire sur les équations aux Dérivées Partielles, 1993-1994, pages Exp. No. X, 10. École Polytech., Palaiseau, 1994.

  92. Stability of resonances under smooth perturbations of the boundary. Asymptotic Anal., 9(3):291-296, 1994. [ DOI ]

  93. Distribution of resonances for the Neumann problem in linear elasticity outside a ball (with G. Vodev). Ann. Inst. H. Poincaré Phys. Théor., 60(3):303-321, 1994. [ http ]

  94. Scattering amplitude is not a finite-rank kernel (with A. G. Ramm). J. Inverse Ill-Posed Probl., 1(4):349-353, 1993. [ DOI ]

  95. Inverse scattering at fixed energy for exponentially decreasing potentials, (with A.G. Ramm). In Inverse problems in mathematical physics (Saariselkä, 1992), volume 422 of Lecture Notes in Phys., pages 189-192. Springer, Berlin, 1993. [ DOI ]

  96. Fixed energy inverse scattering for non-compactly supported potentials (with A.G. Ramm). Math. Comput. Modelling, 18(1):57-64, 1993. [ DOI ]

  97. A three-dimensional Ambartsumian-type theorem (wuth A. G. Ramm). Appl. Math. Lett., 5(5):87-88, 1992. [ DOI ]

  98. Generic uniqueness for two inverse problems in potential scattering. Comm. Partial Differential Equations, 17(1-2):55-68, 1992. [ DOI ]

  99. Some inverse problems in potential scattering. In Integral equations and inverse problems (Varna, 1989), volume 235 of Pitman Res. Notes Math. Ser., pages 258-263. Longman Sci. Tech., Harlow, 1991.

  100. Inverse scattering problem for moving obstacles. Math. Z., 207(3):461-480, 1991. [ DOI ]

  101. Inverse scattering problems for the wave equation with time dependent impurities. In Inverse methods in action (Montpellier, 1989), Inverse Probl. Theoret. Imaging, pages 212-226. Springer, Berlin, 1990.  [ pdf ] [ DOI ]

  102. Stability of the inverse problem in potential scattering at fixed energy. Ann. Inst. Fourier (Grenoble), 40(4):867-884, 1990. [ http ]

  103. A uniqueness result for the inverse back-scattering problem. Inverse Problems, 6(6):1055-1064, 1990. [ pdf ] [ http ]

  104. Inverse scattering problem for a class of moving obstacles. C. R. Acad. Bulgare Sci., 42(6):25-27, 1989.

  105. Uniqueness of the multi-dimensional inverse scattering problem for time dependent potentials. Math. Z., 201(4):541-559, 1989. [ DOI ]

  106. Inverse scattering problem for the wave equation with time-dependent potential. J. Math. Anal. Appl., 140(2):351-362, 1989. [ DOI ]

  107. Uniqueness of the three-dimensional inverse scattering problem for time-dependent potentials. Inverse Problems, 5(1):L11-L14, 1989. [ http ]

  108. Spectral and scattering theory for the linear Boltzmann equation in exterior domain. Math. Nachr., 137:63-77, 1988. [ DOI ]

  109. The Newton-Marchenko equation for time-dependent potentials. Inverse Problems, 4(3):921-928, 1988. [ http ]

  110. Uniqueness of the inverse scattering problem for the wave equation with a potential depending on time. Inverse Problems, 4(3):913-920, 1988. [ http ]

  111. Existence of the scattering operator for dissipative hyperbolic systems with variable multiplicities (with V. Georgiev). J. Operator Theory, 19(2):217-241, 1988.

  112. Inverse scattering problem for the wave equation with time-dependent potential. C. R. Acad. Bulgare Sci., 40(11):29-30, 1987.

  113. Spectral and scattering theory for linear Boltzmann equation in exterior domain. C. R. Acad. Bulgare Sci., 40(1):21-23, 1987.

  114. Unicité du problème inverse de diffusion pour l'équation des ondes avec un potentiel dépendant du temps. C. R. Acad. Sci. Paris Sér. I Math., 305(10):411-413, 1987.

  115. Existence of the scattering operator for dissipative hyperbolic systems with variable multiplicity (with V. Georgiev). In Differential equations and applications, I, II (Russian) (Ruse, 1985), pages 659-662. `Angel Kanchev' Tech. Univ., Ruse, 1987.

  116. Existence and completeness of the wave operators for dissipative systems. Serdica, 13(2):126-132, 1987.

  117. Existence and completeness of wave operators for Maxwell equations in inhomogeneous media. C. R. Acad. Bulgare Sci., 38(5):547-550, 1985.

  118. Existence of the wave operators for dissipative systems. C. R. Acad. Bulgare Sci., 37(6):729-731, 1984.

Volumes edited

  1. Tomography and Inverse Transport Theory, Contemp. Math. 559(2011), coedited with Bal, Finch, Kuchment, Schotland and Uhlmann.

  2. Inverse Problems and Applications, a volume dedicated to G. Uhlmann, Contemp. Math. 615(2014), coedited with Vasy and Zworski.

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NSF logoMost of the publications have been supported by NSF.