Yiran Wang

Welcome! I am a Postdoc Scholar at Department of Mathematics, Stanford University. My advisor is Prof. Andàs Vasy. Before, I was an Acting Assistant Professor at University of Washington (with a joint position at IAS, HKUST) working with Prof. Gunther Uhlmann. 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.

Here is my contact information:
  • E-mail: yrw(at)stanford.edu

  • Mailing address:
    Stanford University
    Department of Mathematics
    Building 380, Stanford, CA 94305


Teaching

In 2018 Winter quarter, I will teach
  • Math 131P: Partial Differential Equations

  • Math 175: Functional Analysis.
In 2018 Autumn quarter, I am teaching Math 19: Calculus

In 2018 Summer and Spring quarter, I taught three courses at University of Washington.

Research

My publications and preprints are listed below.
  1. Convolutional neural networks in phase space and inverse problems (with G. Uhlmann)
    Preprint, 2018.

  2. Singularities generated by the triple interaction of semilinear conormal waves (with A. Sá Barreto)
    Submitted, 2018.

  3. Determination of space-time structures from gravitational perturbations (with G. Uhlmann)
    Submitted, 2018.

  4. Nonlinear interaction of waves in elastodynamics and an inverse problem (with M. de Hoop, G. Uhlmann)
    Submitted, 2018.

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

  6. 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.

  7. Determination of vacuum space-times from the Einstein-Maxwell equations (with M. Lassas, G. Uhlmann)
    Submitted, 2017.

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

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

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

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

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

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

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

  15. Resolvent and radiation fields on non-trapping asymptotically hyperbolic manifolds

My presentations and forthcoming ones are listed below.
  1. (New!) Modern Challenges in Imaging in the Footsteps of Allan Cormack, Tuffs University, 08-2019.
  2. (New!) BIRS workshop: Probing the Earth and the Universe with Microlocal Analysis, Banff, 04-2019.
  3. (New!) IPAM workshop: Computational Challenges in Gravitational Wave Astronomy, UCLA, 01-2019.
  4. Bay Area Microlocal Analysis Seminar, UC Berkeley, 11-2018.
  5. AMS Sectional Meeting, University of Michigan-Ann Arbor, 10-2018.
  6. AMS Sectional Meeting, Boston, 04-2018.
  7. AMS Sectional Meeting, Portland, 04-2018.
  8. Spectral and Scattering Theory Seminar, Purdue University, 03-2018.
  9. Workshop on Inverse Problems, Imaging and PDEs, IAS of HKUST, 03-2018.
  10. Analysis Seminear, Stanford University, 02-2018.
  11. Geometry and Analysis Seminar, UC Santa Cruz, 02-2018.
  12. Math+X Symposium, Rice University, 01-2018.
  13. AMS Southeastern Sectional Meeting, University of Central Florida, 09-2017.
  14. Applied Inverse Problem Conference, Hangzhou, China, 05-2017.
  15. Inverse Problem Seminar, University of Washington, 04-2017.
  16. Spectral and Scattering Theory Seminar, Purdue University, 03-2017.
  17. Workshop on Inverse Problems, Imaging and PDEs, IAS at HKUST, 12-2016.
  18. 2nd IPIA-Young Scholar Symposium, National Taiwan University, 11-2016.
  19. Joint Mathematics Meetings, Seattle, 01-2016.
  20. Workshop on inverse problems and related topics, Zhejiang University, China, 12-2015.
  21. Hong Kong Colloquium on inverse problems, Imaging and PDEs, IAS at HKUST, 11-2015.
  22. PDE/Analysis Mini-School, University of North Carolina at Chapel-Hill, 03-2015.
  23. Spectral and Scattering Theory Seminar, Purdue University, 02-2015.

Last updated: 11-2018.