I am an Assistant Professor at Department of Mathematics & Statistics, Auburn University.
Before joining Auburn, I was a SEW Assistant Professor at the mathematics department of UCSD, and my mentor is Prof. Andrej Zlatoš. In June 2019, I completed my PhD at UCLA , under the supervision of Prof. Inwon Kim.

My research interests are: Stochastic homogenization, Reaction-diffusion equations, Free boundary problems, Hamilton Jacobi equations, Regularity problems, and Mean Field Games. Here is my CV (Feb 2023).
 

Teaching

Publications and preprints (sorted by area)

Preprints

• The convergence rate of vanishing viscosity approximations for mean field games, with W. Tang, preprint, submitted, 2023.
   
  
• Policy iteration for the deterministic control problems -- a viscosity approach, with W. Tang, H. V. Tran, preprint, submitted, 2023.
   
  
• Systemic robustness: a mean-field particle system approach, with E. Bayraktar, G. Guo, W. Tang, preprint, submitted, 2022.
   
  
• Regularity of Hele-Shaw Flow with source and drift, with I. Kim, preprint, 2022.
   
  
• Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations, with A. Zlatoš, preprint, submitted, 2022.
   
  
• Subadditive Theorems and First Passage Percolation in Time-Dependent Environments, with A. Zlatoš, preprint, submitted, 2022.
   
  
• Optimal Estimates on the Propagation of Reactions with Fractional Diffusion, with A. Zlatoš, preprint, submitted, 2021.
   
  
• McKean-Vlasov Equations Involving Hitting Times: Blow-ups and Global Solvability, with E. Bayraktar, G. Guo, W. Tang, preprint, submitted, 2020.
   
  

  Publications

• Quantitative Homogenization for Combustion in Random Media, with A. Zlatoš, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear.
   
  
• Exploratory HJB Equations and Their Convergence, with W. Tang, X. Y. Zhou, SIAM J. Control Optim., to appear.
   
  
• Long Time Dynamics for Combustion in Random Media, with A. Zlatoš, Arch. Ration. Mech. Anal., (2021) 1-62.
   
  
• Free Boundary Regularity of the Porous Medium Equation with nonlocal drifts in Dimension One, Calc. Var. Partial Differential Equations, 61(2022) no. 2, 1-35.
   
  
• Continuity Results for Degenerate Diffusion Equations with LqLp Drifts, with S. Hwang, Nonlinear Anal., 211(2021) 112413.
   
  
• Parallel Search for Information in Continuous Time -- Optimal Stopping and Geometry of the PDE, with T. T. Ke, W. Tang, J. M. Villas-Boas, Appl. Math. Optim., 85 (2022) no.2, 1-23.
   
  
• Porous Medium Equation with a Drift: Free boundary Regularity, with I. C. Kim, Arch. Ration. Mech. Anal., 242(2021) no.2, 1177-1228.
   
  
• Regularity Theory for Second Order Integro-PDEs, with C. Mou, Potential Anal., 54(2021) no.2 387-407.
   
  
• Continuity Properties for Divergence Form Boundary Data Homogenization Problems, with W. M. Feldman, Anal. PDE, 12(2019) no.8, 1963-2002.
   
  
• On a Class of Diffusion-Aggregation Equations, Discrete Contin. Dyn. Syst., 40(2020) no.2, 907.
   
  
• Regularity Properties of Degenerate Diffusion Equations with Drifts, with I. C. Kim, SIAM J. Math. Anal., 50(2018) no.4, 4371-4406.
   
  
• On Continuity Equations in Space-Time Domains, Discrete Contin. Dyn. Syst., 38(2018) no.10, 4837-4873.
   
  
• On Homogenization Problems with Oscillating Dirichlet Conditions in Space-Time Domains, J. London Math. Soc., 105 (2022) no. 2, 909-949.
   
  
• Lack of Exponential Decay in Viscoelastic Materials with Voids, with T. Xiao, Systems Control Lett., 63 (2014)39-42.