Yiran Wang

Welcome! I am an Associate Professor at Department of Mathematics, Emory University.

Before joining Emory, I was a Postdoc Scholar at Stanford University working with Prof. András Vasy. I also held positions of Acting Assistant Professor at University of Washington (with a joint appointment at IAS, HKUST), working with Prof. Gunther Uhlmann. I completed my Ph.D. at Purdue University under the supervision of Prof. Antônio Sá Barreto. My research interests are inverse problems, microlocal analysis, 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 2026 Spring semester, I will teach

• Math 344: Differential Geometry


• Math 546: Introduction to Differential Geometry II

In 2025 Spring semester, I taught

• Math 250: Foundations of Mathematics

In 2024 Fall semester, I taught

• Math 250: Foundations of Mathematics

In 2023 Fall semester, I taught

• Math 318: Complex Variables


• Math 545: Introduction to Differential Geometry I

In 2023 Spring semester, I taught

• Math 351: Partial Differential Equations

Research

Manuscripts and preprints:

• On finding gravitational waves from anisotropies of the Cosmic Microwave Background
  


• Recovering asymptotics of potentials from the scattering of relativistic Schrödinger operators (with G. Uhlmann)
  


• Reconstruction of the observable Universe from the integrated Sachs-Wolfe effect (with J. Chung)
  


• A Lipschitz stability for the Calderón problem with small structure-free anisotropy (with J.-N. Wang)
  


• Generic injectivity of the limited angle Radon transform with weights
  


• Rigidity of Lorentzian metrics with the same scattering relations
  


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


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


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

Publications:

• Inverse source problem for the Boltzmann equation in cosmology
  Annales Henri Poincaré, to appear.


• Iterative reconstruction methods for cosmological X-ray tomography (with J. Chung, L. Onisk)
  SIAM Journal on Imaging Sciences Vol.18, No.3 (2025): 1653-1680.


• The distribution of negative eigenvalues of Schrödinger operators on asymptotically hyperbolic manifolds (with A. Sá Barreto) Journal of Spectral Theory 15 (2025): 679-727.


• Robustness of data-driven approaches in limited angle tomography (with Y. Zhong)
  SIAM Journal on Imaging Sciences Vol.18, No.1 (2025): 345-358.


• Identification of nonlinear beam-hardening effects in X-ray tomography
  SIAM Journal on Mathematical Analysis 56.6 (2024): 7290-7305.


• 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, 2024.


• The anisotropic Calderón problem for high fixed frequency (with G. Uhlmann)
  SIAM Journal on Mathematical Analysis 56.3 (2024): 4084-4103.


• Existence of resonances for Schrödinger operators on hyperbolic space (with D. Borthwick)
  Analysis&PDE 17.6 (2024): 2077-2108.


• Recovery of black hole mass from a single quasinormal mode (with G. Uhlmann)
  Communications in Mathematical Physics 401.1 (2023): 925-936.


• Some integral geometry problems for wave equations
  Inverse Problems 38.8 (2022): 084001. (Special issue of Emerging Talents)


• Inverse scattering for critical semilinear wave equations (with A. Sá Barreto, G. Uhlmann)
  Pure and Applied Analysis 4.2 (2022): 191-223.


• Sharp resolvent estimates on non-positively curved asymptotically hyperbolic manifolds
  International Mathematics Research Notices 2022.8 (2022): 6107-6134.


• Streak artifacts from non-convex metal objects in X-ray tomography (with Y. Zou)
  Pure and Applied Analysis 3.2 (2021): 295-318.


• On the light ray transform of wave equation solutions (with A. Vasy)
  Communications in Mathematical Physics 384.1 (2021): 503-532.


• Singularities generated by the triple interaction of semilinear conormal waves (with A. Sá Barreto)
  Analysis&PDE 14.1 (2021): 135-170.


• Convolutional neural networks in phase space and inverse problems (with G. Uhlmann)
  SIAM Journal on Applied Mathematics 80.6 (2020): 2560-2585.


• Determination of space-time structures from gravitational perturbations (with G. Uhlmann)
  Communications on Pure and Applied Mathematics 73.6 (2020): 1315-1367.
  (Top cited article 2020-2021)


• Nonlinear interaction of waves in elastodynamics and an inverse problem (with M. de Hoop, G. Uhlmann)
  Mathematische Annalen 376.1-2 (2020): 765-795.


• 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 Vol.36. No.2 (2019): 347-363.


• Distribution of resonances for analytic asymptotically hyperbolic spaces
  Journal of Spectral Theory 9.2 (2019): 651-675.


• Inverse problems for quadratic derivative nonlinear wave equations (with T. Zhou)
  Communications in Partial Differential Equations 44.11 (2019): 1140-1158.


• The scattering operator on asymptotically hyperbolic manifolds (with A. Sá Barreto)
  Journal of Spectral Theory 9.1 (2019): 269-314.


• Quantitavie analysis of metal artifacts in X-ray tomography (with B. Palacios, G. Uhlmann)
  SIAM Journal on Mathematical Analysis 50.5 (2018): 4914-4936.


• Parametrices for the light ray transform on Minkowski spacetime
  Inverse Problems and Imaging Vol.12, No.1 (2018): 229-237.


• Inverse problems for semilinear wave equations on Lorentzian manifolds (with M. Lassas, G. Uhlmann)
  Communications in Mathematical Physics 360.2 (2018): 555-609.


• Reducing streaking artifacts in quantitative susceptibility mapping (with B. Palacios, G. Uhlmann)
  SIAM Journal on Imaging Sciences Vol.10, No.4 (2017): 1921-1934.


• The semiclassical resolvent on conformally compact manifolds with variable curvature at infinity (with A. Sá Barreto)
  Communications in Partial Differential Equations 41.8 (2016): 1230-1302.

Last updated: 10-2025.