Novikov Roman Gennadievich

In 1986 he graduated from the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University. In 1989 he defended his Ph.D. thesis at the Faculty of Mechanics and Mathematics of MSU; topic – “The inverse scattering problem for the two-dimensional Schrödinger equation at a fixed energy and nonlinear equations”; scientific adviser – S.P. Novikov. He defended his doctoral dissertation in 1998 at the St. Petersburg Branch of V.A. Steklov Mathematical Institute; topic – “Multidimensional inverse scattering problem and applications”.

Professional experience. Since 1990 he has been working at the Institute of earthquake prediction theory and mathematical geophysics of the Russian Academy of Sciences (IEPT RAS), currently in the position of Chief Researcher. Since 1992 he has been working at the National Center for Scientific Research of France (CNRS), currently in the position of Directeur de Recherche.

Areas of professional interest: direct and inverse scattering problems, tomography, soliton theory.

Educational activity. R.G. Novikov’s video course “Tomography and the inverse scattering problem” and other reports can be listened to at the link.

Former PhD students: A. Jollivet, A.V. Kazeykina, M. Santacesaria, M.I. Isaev, A.D. Agaltsov, F.O. Goncharov.

Participant of RFBR grants. Co-head of the Franco-Russian project PRC n°1545 CNRS/RFBR: “Équations quasi-linéaires, problèmes inverses et leurs applications”, 2017–2019.

Identifiers

Scopus Author ID: 6603393652

Web of Science Researcher ID: M-4721-2013

ORSID ID: 0000-0003-3346-9414

Researchgate

Key publications
  • M. Isaev, R.G. Novikov, Hölder-logarithmic stability in Fourier synthesis, Inverse Problems 36(12), 125003 (17 pp) (2020).
  • R.G. Novikov, Multipoint formulas for scattered far field in multidimensions, Inverse Problems 36, 095001 (12 pp) (2020).
  • A.D. Agaltsov, T. Hohage, R.G. Novikov, Global uniqueness in a passive inverse problem of helioseismology, Inverse Problems 36(5), 055004 (21 pp) (2020).
  • P.G. Grinevich, R.G. Novikov, Moutard transforms for the conductivity equation, Letters in Mathematical Physics 109(10), 2209–2222 (2019).
  • A.D. Agaltsov, T. Hohage, R.G. Novikov, An iterative approach to monochromatic phaseless inverse scattering, Inverse Problems 35(2), 024001 (34 pp) (2019).
  • R.G. Novikov, Non-abelian Radon transform and its applications, In The first 100 years of the Radon Transform, R. Ramlau, O. Scherzer (Eds.) (Chapter 5, pp. 115–128) De Gruyter, 2019.
  • F.O. Goncharov, R.G. Novikov, A breakdown of injectivity for weighted ray transforms in multidimensions, Arkiv för Matematik 57(2), 333–371 (2019).
  • R.G. Novikov, I.A. Taimanov, Darboux–Moutard transformations and Poincaré–Steklov operators, Proc. Steklov Inst. Math. 302, 315–324 (2018).
  • A.D. Agaltsov, T. Hohage, R.G. Novikov, Monochromatic identities for the Green function and uniqueness results for passive imaging, SIAM J. Appl. Math. 78(5), 2865–2890 (2018).
  • R.G. Novikov, I.A. Taimanov, Moutard type transformation for matrix generalized analytic functions and gauge transformations, Russian Math. Surveys 71(5), 970–972 (2016).
  • P.G. Grinevich, R.G. Novikov, Moutard transform for generalized analytic functions, Journal of Geometric Analysis 26(4), 2984–2995 (2016).
  • E.L. Lakshtanov, R.G. Novikov, B.R. Vainberg, A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy, Rend. Istit. Mat. Univ. Trieste 48, 21–47 (2016).
  • R.G. Novikov, Formulas for phase recovering from phaseless scattering data at fixed frequency, Bulletin des Sciences Mathématiques 139(8), 923–936 (2015).
  • R.G. Novikov, Inverse scattering without phase information, Séminaire Laurent Schwartz – EDP et applications, (2014–2015), Exp. No16, 13pp.
  • R.G. Novikov, An iterative approach to non-overdetermined inverse scattering at fixed energy, Sb. Math. 206(1), 120–134 (2015).
  • A.D. Agaltsov, R.G. Novikov, Riemann-Hilbert problem approach for two-dimensional flow inverse scattering, Journal of Mathematical Physics 55, 103502 (25 pp) (2014).
  • R.G. Novikov, I.A. Taimanov, S.P. Tsarev, Two-dimensional von Neumann–Wigner potentials with a multiple positive eigenvalue, Funct. Anal. Appl. 48(4), 295–297 (2014).
  • R.G. Novikov, M. Santacesaria, Monochromatic reconstruction algorithms for the two-dimensional multi-channel inverse problems, International Mathematics Research Notes 2013(6), 1205–1229 (2013).
  • R.G. Novikov, New global stability estimates for the Gel’fand-Calderon inverse problem, Inverse Problems 27, 015001 (21 pp) (2011).
  • R.G. Novikov, The d-bar approach to approximate inverse scattering at fixed energy in three dimensions, International Mathematics Research Papers 2005(6), 287–349 (2005).
  • R.G. Novikov, An inversion formula for the attenuated X-ray transformation, Arkiv för Matematik 40(1), 145–167 (2002).
  • R.G. Novikov, On determination of a gauge field on R^d from its non-abelian Radon transform along oriented straight lines, Journal of the Institute of Mathematics of Jussieu 1(4), 559–629 (2002).
  • R.G. Novikov, Small angle scattering and X-ray transform in classical mechanics, Arkiv för Matematik 37(1), 141–169 (1999).
  • P.G. Grinevich, R.G. Novikov, Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials, Communications in Mathematical Physics 174, 409–446 (1995).
  • R.G. Novikov, The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential, Communications in Mathematical Physics 161, 569–595 (1994).
  • R.G. Novikov, The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator, J. Funct. Anal. 103(2), 409–463 (1992).
  • R.G. Novikov, Multidimensional inverse spectral problem for the equation −Δψ+(v(x)−Eu(x))ψ=0, Funct. Anal. Appl. 22(4), 263–272 (1988).
  • G.M. Henkin, R.G. Novikov, The ∂¯-equation in the multidimensional inverse scattering problem, Russian Math. Surveys 42(3), 109–180 (1987).

Presentations at the Conferences. As an invited speaker R.G. Novikov participated in more than 70 conferences in the USSR, Russia, France, USA, Canada, Austria, Bulgaria, England, Germany, Greece, Malta, Norway, Portugal, Sweden, Turkey.

Participation in editorial boards of journals. R.G. Novikov is member of the editorial boards of the journals: Inverse Problems since 2001 (International Advisory Panel since 2015); Journal of Inverse and Ill-Posed Problems since 2008; Eurasian Journal of Mathematical and Computer Applications (EJMCA) since 2013; Inverse Problems in Science and Engineering since 2013; Journal of Geometric Analysis since 2015; Journal of Applied and Industrial Mathematics since 2018.

Membership in unions and associations. R.G. Novikov is member of the Eurasian Association on Inverse Problems (EAIP) and member of the Institute of Physics (IOP), London.

Awards. R.G. Novikov was awarded the prize of the National Center for Scientific Research of France “Prime d’excellence scientifique du CNRS” (2012) and the letter of gratitude from the Department of Earth Sciences of the Russian Academy of Sciences (Resolution of the Bureau of the Department of Earth Sciences of RAS 13000/97 of November 26, 2019).