Yiran Wang

Welcome! I am an Assistant Professor at Department of Mathematics, Emory University. Before, I was a Postdoc Scholar at Stanford University working with Prof. András Vasy. I also worked with Prof. Gunther Uhlmann as an Acting Assistant Professor at University of Washington (with a joint position at IAS, HKUST). I obtained my Ph.D from Purdue University under the supervision of Prof. Antônio Sá Barreto.

My research interests are microlocal analysis, inverse problems, integral geometry, spectral and scattering theory.

I am a member of the Inverse Problems International Association (IPIA).

I am on the Editorial Board of the journal Communications on Analysis and Computation.

Here is my contact information:
  • E-mail: yiran.wang(at)emory.edu

  • Office: Mathematics & Science Center, E414.

  • Mailing address:
    Department of Mathematics
    400 Dowman Drive
    Atlanta, GA 30322


Teaching

In 2025 Spring semester, I will teach In 2024 Fall semester, I am teaching In 2023 Fall semester, I taught In 2023 Spring semester, I taught

Research

  • Inverse problems in cosmological X-ray tomography
        Microlocal Analysis and Inverse Problems in Tomography and Geometry
        Radon Series on Computational and Applied Mathematics, Volume 30.

  • The distribution of negative eigenvalues of Schrödinger operators on asymptotically hyperbolic manifolds (with A. Sá Barreto)
        Submitted.

  • Rigidity of Lorentzian metrics with the same scattering relations
        Submitted.

  • Iterative reconstruction methods for cosmological X-ray tomography (with J. Chung, L. Onisk)
        Submitted.

  • Robustness of data-driven approaches in limited angle tomography (with Y. Zhong)
        SIAM Journal on Imaging Sciences, to appear.

  • Inverse source problem for the Boltzmann equation in cosmology
        Submitted.

  • Identification of nonlinear beam-hardening effects in X-ray tomography
        SIAM Journal on Mathematical Analysis, to appear.

  • Recovery of black hole mass from a single quasinormal mode (with G. Uhlmann)
        Communications in Mathematical Physics.

  • Existence of resonances for Schrödinger operators on hyperbolic space (with D. Borthwick)
        Analysis and PDE.

  • Some integral geometry problems for wave equations
        Inverse Problems, special issue of Emerging Talents.

  • Microlocal analysis of the light ray transform on globally hyperbolic Lorentzian manifolds
        Submitted.

  • The anisotropic Calderón problem for high fixed frequency (with G. Uhlmann)
        SIAM Journal on Mathematical Analysis.

  • Inverse scattering for critical semilinear wave equations (with A. Sá Barreto, G. Uhlmann)
        Pure and Applied Analysis.

  • Streak artifacts from non-convex metal objects in X-ray tomography (with Y. Zou)
        Pure and Applied Analysis.

  • Sharp resolvent estimates on non-positively curved asymptotically hyperbolic manifolds
        International Mathematics Research Notices (IMRN).

  • On the light ray transform of wave equation solutions (with A. Vasy)
        Communications in Mathematical Physics.

  • Convolutional neural networks in phase space and inverse problems (with G. Uhlmann)
        SIAM Journal on Applied Mathematics.

  • Singularities generated by the triple interaction of semilinear conormal waves (with A. Sá Barreto)
        Analysis and PDE.

  • Determination of space-time structures from gravitational perturbations (with G. Uhlmann)
        Communications on Pure and Applied Mathematics.
        (Top cited article 2020-2021)

  • Nonlinear interaction of waves in elastodynamics and an inverse problem (with M. de Hoop, G. Uhlmann)
        Mathematische Annalen.

  • Quantitavie analysis of metal artifacts in X-ray tomography (with B. Palacios, G. Uhlmann)
        SIAM Journal on Mathematical Analysis.

  • Nonlinear responses from the interaction of two progressing waves at an interface (with M. de Hoop, G. Uhlmann)
        Annales de l'Institut Henri Poincaré, Analyse Non Linéaire.

  • Determination of vacuum space-times from the Einstein-Maxwell equations (with M. Lassas, G. Uhlmann)
        Submitted.

  • Distribution of resonances for analytic asymptotically hyperbolic spaces
        Journal of Spectral Theory.

  • Parametrices for the light ray transform on Minkowski spacetime
        Inverse Problems and Imaging.

  • Inverse problems for quadratic derivative nonlinear wave equations (with T. Zhou)
        Communications in Partial Differential Equations.

  • Reducing streaking artifacts in quantitative susceptibility mapping (with B. Palacios, G. Uhlmann)
        SIAM Journal on Imaging Sciences.

  • The scattering operator on asymptotically hyperbolic manifolds (with A. Sá Barreto)
        Journal of Spectral Theory.

  • Inverse problems for semilinear wave equations on Lorentzian manifolds (with M. Lassas, G. Uhlmann)
        Communications in Mathematical Physics.

  • The semiclassical resolvent on conformally compact manifolds with variable curvature at infinity (with A. Sá Barreto)
        Communications in Partial Differential Equations.

  • Resolvent and radiation fields on non-trapping asymptotically hyperbolic manifolds
       

    • Recent and upcoming presentations:

  • AMS Spring Southeastern Sectional Meeting, Florida State University, Tallahassee, 03-2024.
  • AMS Spring Eastern Sectional Meeting, Howard University, Washington DC, 04-2024.
  • SIAM Conference on Imaging Science, Atlanta, 05-2024.
  • CBMS Conference on Inverse Problems and Nonlinearity, Clemson University, 06-2024.
  • International Conference and School on Inverse Problems, Shanghai Center for Mathematical Sciences, Shanghai, 06-2024
  • BIRS workshop "Partial Differential Equations: Deterministic and Probabilistic", Hangzhou, 08-2024.


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    Last updated: 08-2024.