Kui Ren

Professor of Applied Mathematics
Department of Applied Physics & Applied Mathematics and the Data Science Institute

Columbia University

215 S. W. Mudd Building

500 W 120th Street

New York, NY 20017


Tel: 212-854-4731

Email: kr2002@columbia.edu


I am interested in applied and computational mathematics in general. My recent research topics include: inverse problem theory, computation and applications; mathematics of new imaging modalities; fast algorithms for PDEs; kinetic modeling; random graphs and complex networks; computational optimization

Here are some recent preprints/reprints (a full list can be found here; some of the simplified versions of the computational codes we developed can be found at Github):

 Separability of the kernel function in an integral formulation for anisotropic radiative transfer (with H. Zhao and Y. Zhong), Submitted, 2019. [pdf].

 Unique determination of absorption coefficients in a semilinear transport equation (with Y. Zhong), Submitted, 2020. [pdf].

 Imaging point sources in heterogeneous (with Y. Zhong), Inverse Problems, 35: 125003, 2019. [pdf].

 The quadratic Wasserstein metric for inverse data matching, Inverse Problems, 36:055001, 2020. [pdf].

 A fast algorithm for radiative transport in isotropic media (with R. Zhang and Y. Zhong), J. Comput. Phys., 2019. [pdf].

An implicit boundary integral method for computing electric potential of macromolecules in solvent (with R. Tsai and Y. Zhong), J. Comput. Phys., 359:199-215, 2018. [pdf].

Image reconstruction in quantitative PAT with the simplified P2 model (with C. Frederick and S. Vallelian), SIAM J. Imag. Sci., 11:2847-2876, 2018. [pdf].

Characterizing the impact of model uncertainties in quantitative photoacoustics (with S. Vallelian), SIAM/ASA J Uncertainty Quantification, 8:636-667, 2020. [pdf].

 Surface effects in dense random graphs with sharp edge constraint (with C. Radin and L. Sadun), Preprint, 2017. [pdf].

 Quantitative photo-acoustic imaging of two-photon absorption, (with P. Bardsley and R. Zhang), J. Biomed. Opt., 23, 016002, 2018. [pdf].

 A global stability estimate for the photo-acoustic inverse problem in layered media, (with F. Triki), European J. Appl. Math., In Press, 2018. [pdf].

 The phases of large networks with edge and triangle constraints, (with R. Kenyon, C. Radin and L. Sadun), J. Phys. A: Math. Theor., 50, 435001, 2017. [pdf].

 Nonlinear quantitative photoacoustic tomography with two-photon absorption (with R. Zhang), SIAM J. Appl. Math., 78, 479-503, 2018. [pdf].

 A symmetry breaking transition in the edge/triangle network model (with C. Radin and L. Sadun), AIHP-D, 5:251-286, 2018. [pdf].

 Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells (with M. Harmon and I. M. Gamba), J. Comput. Phys., 327, 140-167, 2016. [pdf ].

 Inverse transport problems in quantitative PAT for molecular imaging (with R. Zhang and Y. Zhong), Inverse Problems, 31, 125012, 2015. [pdf].

 Bipodal structure in oversaturated random graphs (with R. Kenyon, C. Radin and L. Sadun), Int. Math. Res. Notices, 2016, 1-36, 2016. [pdf].

 On the modeling and simulation of reaction-transfer dynamics in semiconductor-electrolyte solar cells (with Y. He, I. M. Gamba and H. Lee), SIAM J. Appl. Math., 75, 2515-2539, 2015. [pdf].

 A one-step reconstruction algorithm for quantitative photoacoustic imaging (with T. Ding and S. Vallelian), Inverse Problems, 31, 095005, 2015. [pdf]. This paper was selected as by Inverse Problems as one of the papers in its collection: Highlight of 2015

 Multipodal Structure and Phase Transitions in Large Constrained Graphs (with R. Kenyon, C. Radin and L. Sadun), J. Stat. Phys., 168, 233-258, 2017. [pdf].     

 The Asymtotics of Large Constrained Graphs (with C. Radin and L. Sadun), J. Phys. A: Math. Theor. 47, 175001, 2014. [pdf]. One figure in the paper appears on the cover of the journal.

 Quantitative photoacoustic imaging in the radiative transport regime (with A. Mamonov), Commun. Math. Sci, 12, 201-234, 2014. [pdf].

 Inverse transport calculations in optical imaging with subspace optimization algorithms (with T. Ding), J. Comput. Phys., 273, 212-226, 2014 [pdf]

 Quantitative fluorescence photoacoustic tomography (with H. Zhao), SIAM J Imag. Sci., 6, 2404-2429, 2013. [pdf]

 A hybrid reconstruction method for quantitative PAT (with H. Gao and H. Zhao), SIAM J. Imag. Sci., 6, 32-55, 2013. [pdf]

 On multi-spectral quantitative photoacoustic tomography (with G. Bal), Inverse Problems, 28, 025010, 2012. [pdf]. This paper was selected as a featured article by Inverse Problems and then chosen to be included in its collection Highlight of 2012


The Applied Mathematics Research Group at Columbia: Applied Mathematics Colloquium Probability Seminar Mathematics Colloquium


The Data Science Institute at Columbia: Data Science Colloquium


If you have a PhD in mathematics but forget already who your thesis advisor was, you can probably figure it out here

Last updated: July 2018

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