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.
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.
The phases of large networks with edge and triangle constraints, (with R. Kenyon, C. Radin and L. Sadun), Preprint, 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), Submitted, 2015. [pdf].
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 2012
Quantitative Thermo-acoustics and related problems (with G. Bal, G. Uhlmann and T. Zhou), Inverse Problems, 27, 055007, 2011. [pdf].
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 Erdös 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
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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