Kui Ren

Professor of Applied
Mathematics

Department
of Applied Physics and Applied Mathematics

215 S. W. Mudd Building

500 W 120^{th} Street

New York, NY 20017

Tel: 212-854-4731

Email: kr2002@columbia.edu

I am
currently on leave from Department of
Mathematics, The University of Texas at
Austin.

I am
interested in applied and computational mathematics in general. My recent
research topics include: inverse problems, mathematics of imaging, fast
algorithms, kinetic modeling, and random graphs and complex networks.

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 here):

· 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].

· Imaging
point sources in heterogeneous (with Y. Zhong), *Submitted, *2018. [pdf].

· Image reconstruction in quantitative PAT with the simplified P_{2}
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), *Submitted, *2018. [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 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), *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.

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