Kui Ren |
Research |

I am associated with the Department of Mathematics and the Institute for Computational Engineering and Sciences (ICES) in the University of Texas at Austin. I got my PhD from Columbia University in 2006 and spent a year in The University of Chicago as a L. E. Dickson instructor in Applied Mathematics before joining UT Austin in Fall 2008. Her is a full vita.

I am interested in applied and computational mathematics in general. My recent research are mainly on: inverse problems to PDEs, mathematical imaging, kinetic equations, and random graphs. Below are some of my recent publications. A full list of my publications can be found here.

A global stability estimate for the photo-acoustic inverse problem in layered media, (with F. Triki),

*Submitted*, 2017. [pdf].The phases of large networks with edge and triangle constraints, (with R. Kenyon, C. Radin and L. Sadun),

*Submitted*, 2017. [pdf].Nonlinear quantitative photoacoustic tomography with two-photon absorption (with R. Zhang),

*Submitted*, 2016. [pdf].A fast algorithm for radiative transport in isotropic media (with R. Zhang and Y. Zhong),

*Submitted*, 2016. [pdf].A symmetry breaking transition in the edge/triangle network model (with C. Radin and L. Sadun),

*Submitted*, 2016. [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].

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.**,*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 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].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 2012Quantitative Thermo-acoustics and related problems (with G. Bal, G. Uhlmann and T. Zhou),

*Inverse Problems*, 27, 055007, 2011. [pdf].Multiple-source quantitative photoacoustic tomography (with G. Bal),

*Inverse Problems*, 27, 075003, 2011. [pdf]. Read the news about this paper from Inverse Problems.Non-uniqueness result for a hybrid inverse problem (with G. Bal),

*Contemporary Mathematics*, 2011. [pdf].Recovering doping profiles in semiconductor devices with the Boltzmann-Poisson model (with Y. Cheng and I. M. Gamba),

*J. Comput. Phys.,*230, 3391-3412, 2011*.*[pdf].Recent development in numerical techniques for transport-based medical imaging methods,

*Commun. Comput. Phys.,*8, 1-50, 2010*.*[pdf].Parametric image reconstruction using the discrete cosine transform for optical tomography (with X. Gu, J. Masciotti and A. H. Hilescher),

*J. Biomed. Opt.,*14, 064003, 2009*.*[pdf].Physics-based models for measurement correlations. Application to an inverse Sturm-Liouville problem (with G. Bal),

*Inverse Problems,*25, 055006, 2009*.*[pdf].Transport-based imaging in random media (with G. Bal),

*SIAM Applied Math.,*68, 1738-1762, 2008*.*[pdf].Experimental validation of a transport-based imaging method in highly scattering environments (with G. Bal, L. Carin and D. Liu),

*Inverse Problems,*23, 2527-2539, 2007*.*[pdf].Transport- and diffusion-based optical tomography in small domain: A comparative study (with G. Bal and A. H. Hilescher),

*Applied Optics,*46, 6669-6679, 2007*.*[pdf].Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer (with X. Gu and A. Hielscher), Appl. Optics, 46, 1624-1632, 2007. [pdf].

Frequency domain optical tomography based on the equation of radiative transfer (with G. Bal and A. H. Hielscher),

*SIAM J. Sci. Comput.,*28, 1463-1489, 2006*.*[pdf].Reconstruction of singular surfaces by shape sensitivity analysis and level set method (with G. Bal), Math. Models Methods Appl. Sci. (M3AS)

*,*16, 1347-1373, 2006*.*[pdf].Optical tomographic imaging as a PDE-constrained optimization problem (with G. Abdoulaev and A. H. Hielscher),

*Inverse Problems,*21, 1507-1530, 2005. [pdf].Atmospheric concentration profile reconstructions from radiation measurements (with G. Bal),

*Inverse Problems,*21, 153-168, 2005. [pdf].Algorithm for solving the equation of radiative transfer in the frequency domain (G. S. Abdoulaev, G. Bal and A. H. Hilescher),

*Optics Lett.,*29, 578-580, 2004*.*[pdf].Generalized diffusion model in optical tomography with clear layers (with G. Bal),

*J. Opt. Soc. Am. A,*20, 2355-2364, 2003*.*[pdf].

My ErdÃ¶s number is 4 according to MathSciNet of American Mathematical Society.

Here are some useful links inside UT Austin: Mathematics Center for Numerical Analysis ICES TACC

Here are links to NSF-supported math institutes: AIM ICERM IMA IPAM MBI MSRI SAMSI

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

Last updated: July 2013 |
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