研究领域

偏微分方程、应用数学

教育背景

2002-2006 学士 北京大学
2006-2011 博士 美国哥伦比亚大学

工作经历

2016  至今 助理教授   清华大学丘成桐数学科学中心
2013-2016  Dickson Instructor, 美国芝加哥大学
2011-2013 博士后 法国巴黎高等师范学院


荣誉与奖励

2019年 第八届华人数学家大会45分钟邀请报告

2018年 国家自然科学基金委青年基金 (独立PI)

2016年 第七届华人数学家大会45分钟邀请报告
2015年 美国自然科学基金委NSF Grant (独立PI)

发表论文

Papers and preprints

  1. Convergence rate for the homogenization of stationary diffusions in dilutely perforated domains with reflecting boundaries. [arXiv:2108.08533] Preprint (2021), submitted.


  2. High order homogenized Stokes models capture all three regimes. (with F. Feppon). [HAL-03098222] Preprint (2021), submitted.


  3. Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes. [arXiv:2007.03333][Journal] Calculus of Variations and PDEs 60, 2 (2021).


  4. Effective Fronts of Polytope Shapes. (with H. V. Tran and Y. Yu). [arXiv:1909.11067] Minimax Theory and its Applications5 (2020), no. 2, 347--360.


  5. Generalized Ergodic Problems: Existence and Uniqueness Structures of Solutions. (with H. Mitake and H. V. Tran). [arXiv:1902.05034] J. Differential Equations268 (2020), no. 6, 2886--2909.


  6. A unified homogenization approach for the Dirichlet problem in perforated domains. [arXiv:1901.08251]SIAM J. Math. Anal. 52 (2020), no.2, 1192--1220.


  7. A backscattering model based on corrector theory of homogenization for the random Helmholtz equation. (with O. Pinaud[arXiv:1805:02822]DCDS-B 24 (2019), no. 10, 5377--5407.


  8. Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment. (with P. E. Souganidis and H. V. Tran). [arXiv:1606.06409] Research in the Mathematical Sciences (2017), Paper No. 6, 20pp.


  9. Inverse problems, non-roundedness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model. (with H. V. Tran and Y. Yu[arXiv:1602.04728] Nonlinearity30 (2017), no. 5, 1853--1875.


  10. Homogenization of interfaces moving in spatially random temporally periodic environment. (with P. E. Souganidis and H. V. Tran). [mathscidoc:1806.03001] Preprint (2016)


  11. Fluctuations in the Homogenization of Semilinear Equations with Random Potentials. (with G. Bal[arXiv:1509.05321] Comm. Partial Differential Equations42 (2016), no.12, pp. 1839--1859.


  12. Limiting distribution of elliptic homogenization error with periodic diffusion and random potential. [arXiv:1505.02721] Analysis & PDE9 (2016), no. 1, pp. 193--228.


  13. Large time average of reachable sets and Applications to Homogenization of interfaces moving with oscillatory spatio-temporal velocity. (with P. E. Souganidis and H. V. Tran[arXiv:1408.2013] DCDS-S 11 (2018), no.5, 915--939.


  14. Homogenization of Randomly Deformed Conductivity Resistant Membranes, [arXiv:1406.0580] Commun. Math. Sci.14 (2016), no.5, 1237--1268.


  15. Spectroscopic imaging of a dilute cell suspension. (with H. AmmariJ. GarnierL. Giovangigli and J.K. Seo), [PDF] J. Math. Pures Appl. 105 (2016), no.5, 603--661.


  16. Localization, stability and resolution of topological derivative based imaging functionals in elasticity. (with H. AmmariE. BretinJ. Garnier, H. Kang and A. Wahab), [arXiv:1210.6760] SIAM J. Imaging Sci. 6 (2013), no. 4, 2174-2212.


  17. Passive array correlation based imaging in weakly random waveguide. (with H. Ammari and J. Garnier), [arXiv:1211.0682] Multiscale Modeling and Simulation11 (2013), no.2, pp. 656-681.


  18. Corrector analysis of a heterogeneous multi-scale scheme for elliptic equations with random potential. (with G. Bal), [arXiv:1209.4974] Mathematical Modeling and Numerical Analysis (M2AN)48 (2014), no. 2, 387-409.


  19. Radiative transfer and diffusion limits for wave field correlations in locally shifted random media. (with H. AmmariE. BossyJ. Garnier and L. Seppecher), [arXiv:1207.1604] J. Math. Phys. 54 (2013), 021501.


  20. Target identification using dictionary matching of Generalized Polarization Tensors. (with H. AmmariT. BoulierJ. GarnierH. Kang and H. Wang), [arXiv:1204.3035] Found. Comput. Math.14 (2014), no. 1, 27-62.


  21. Quantitative thermo-acoustic imaging: an exact formula. (with H. AmmariJ. Garnier and L. Nguyen), [arXiv:1201.0619] J. Differential Equations254 (2013), No.3, pp. 1375--1395.


  22. Resolution and stability analysis in acousto-electric imaging. (with H. Ammari and J. Garnier), [PDF] Inverse Problems 28 (2012), 084005.


  23. Corrector theory for elliptic equations with oscillatory and random potentials with long range correlations. (with G. BalJ. Garnier and Y. Gu), [PDF] Asymptotic Analysis77 (2012), No. 3-4, pp. 123-145.


  24. Corrector theory for MsFEM and HMM in random media. (with G. Bal), [PDF] [Journal] Multiscale Modeling and Simulation 9 (2011), pp. 1549-1587.


  25. Corrector theory for elliptic equations in random media with singular Green's function (with G. Bal), [PDF] [Journal] Commun. Math. Sci. 9 (2011), No. 2, pp. 383-411.


  26. Homogenization and Corrector Theory for Linear Transport in Random Media (with G. Bal), [PDF] [Journal] Discrete Contin. Dyn. Syst. 28 (2010), No. 4, 1311-1343.


  27. Fluctuation theory for radiative transfer in random media (with G. Bal), [PDF] [Journal] Journal of Quantitative Spectroscopy & Radiative Transfer112 (2011), No. 4, pp. 660-670.

Book


  1. Mathematical and Statistical Methods for Multistatic Imaging. (with H. AmmariJ. Garnier, H. Kang, M. LimK. Solna, and H. Wang), Lecture Notes in Mathematics, Springer-Verlag, Cham, 2013.

Book Chapters


  1. Uncertainty modeling and propagation in linear kinetic equations, (with G. Bal and O. Pinaud), in Uncertainty quantification for hyperbolic and kinetic equations, pp. 59--92, SEMA-SIMAI Springer Ser., 14, Springer, Cham 2017.

Conference Proceedings


  1. On the homogenization of a front propagation model in oscillatory environmentsProceedings of the 8th ICCM, preprint 2019, submitted.