Invited Talks

1. Special Session: Dynamics and Variational Methods of Quasi-Hamiltonian Systems Jul 06–10, 2026
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   15th AIMS Conference, Athens, Greece
28. Rates of Vanishing Viscosity for Hamilton–Jacobi Equations with State Constraints Feb 26, 2026
    abstract   ·   web
    PDE Geometric Analysis seminar, University of Wisconsin - Madison
We study state-constraint boundary conditions arising in optimal control problems, where the system state is confined to a prescribed domain. Introducing noise leads to a stochastic control problem whose value function also satisfies a state-constraint condition and converges to the deterministic solution as the noise vanishes. Unlike the deterministic case, the stochastic behavior depends on whether the Hamiltonian has subquadratic or superquadratic growth. After briefly reviewing the subquadratic case, we focus on the superquadratic regime and establish convergence rates of the value function in terms of the noise magnitude. In particular, beyond the general rate, we prove a better one-sided rate under semiconcavity assumptions. The proofs rely on new barrier constructions and optimal control arguments, as state-constraint solutions are delicate and not semiconcave up to the boundary.
29. Special Session on Advances and challenges in hyperbolic conservation laws Oct 25, 2025
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    Fall 2025 AMS Eastern Virtual Sectional Meeting
30. Special Session on Recent Advances in Numerical Methods for ODE/PDEs and Their Applications Oct 04–05, 2025
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    Fall 2025 AMS Southeastern Sectional Meeting, New Orleans, LA
31. (Online) Mitake–Tran PDE reading seminar, UW–Madison Oct 01, 2025
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    Rates of Vanishing Viscosity for Hamilton–Jacobi Equations with State Constraints
32. Baylor Applied Math Seminar Sep 08, 2025
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    Baylor University, Department of Mathematics
33. Workshop on Partial Differential Equations, Mathematical Physics and Numerics 2025 Aug 16–17, 2025
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    Texas A&M University, Department of Mathematics
34. (Withdrawn) Workshop: Recent progress in Hamilton-Jacobi equations and related topics Jun 02, 2025
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    Nanjing, China
35. PDEs Seminar, University of Tennessee – Knoxville Nov 07, 2024
    archive   ·   web
    Convergence Rate for 1D Quasi-Periodic Homogenization of Hamilton–Jacobi Equations
36. Colloquium, Minnesota State University – Mankato Oct 29, 2024
    Regularity and Vanishing Viscosity Rates in the Ergodic Problem
37. Analysis Seminar, University of Maryland, College Park Oct 24, 2024
    archive   ·   web
    Convergence Rate for 1D Quasi-Periodic Homogenization of Hamilton–Jacobi Equations
38. Analysis and PDE seminar, Michigan State University (MSU) Oct 16, 2024
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    Regularity and Vanishing Viscosity Rates in the Ergodic Problem
39. (Online) Analysis Seminar, Texas Tech University (TTU) Oct 14, 2024
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    Remarks on the well-posedness of Viscosity Solutions for the One-Phase Muskat Problem
40. Summer school in PDE and Application 2024 Jul 27, 2024
    schedule   ·   web
    Vietnam Institute for Advanced Study in Mathematics (VIASM), Saigon University (SGU)
    Remarks on the well-posedness of Viscosity Solutions for the One-Phase Muskat Problem
    bulletin - eng   ·   pdf   ·   bulletin - vie   ·   pdf
41. (Online) PDE reading seminar, UW-Madison May 30, 2024
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    Polynomial convergence rate for quasiperiodic homogenization of Hamilton-Jacobi equations
42. Analysis and PDE seminar, Michigan State University (MSU) Apr 17, 2024
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    Convergence Rate for 1D Quasi-Periodic Homogenization of Hamilton-Jacobi Equations
43. PDEs seminar, Ohio State University (OSU) Apr 09, 2024
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    Properties of the effective Hamiltonian and homogenization of the Hamilton-Jacobi equation
44. (Online) Early Career Math Colloquium, The University of Arizona Mar 21, 2024
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    Properties of the effective Hamiltonian and homogenization of the Hamilton-Jacobi equation
45. Differential Equations and Nonlinear Analysis Seminar, North Carolina State University Nov 08, 2023
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    Generalized Convergence of Hamilton–Jacobi equations with state-constraint
46. SIAM Great Lakes 2023, Mini Symposium, Michigan State University Oct 15, 2023
    program   ·   web
    Nonlinear partial differential equations and optimal transport with applications
    Generalized Convergence of Hamilton–Jacobi equations with state-constraint
47. Applied Analysis Seminar, Tsinghua University, Beijing, China Aug 03, 2023
    Generalized Convergence of Hamilton–Jacobi equations
48. Analysis Seminar, University of Science, VNU-HCMC Jun 20, 2023
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    Generalized Convergence of Hamilton–Jacobi equations
49. Madison PDEs Conference, University of Wisconsin – Madison May 23, 2023
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    Generalized Convergence of Hamilton–Jacobi equations
50. (Online) Chinese Academy of Sciences, Academy of Mathematics and Systems Science Apr 26, 2023
    link   ·   slides
    The regularity with respect to domains of the additive eigenvalues of superquadratic Hamilton–Jacobi equation
51. (Online) Chinese Academy of Sciences, Academy of Mathematics and Systems Science Apr 19, 2023
    link   ·   slides
    Remarks on the vanishing viscosity process of state-constraint Hamilton-Jacobi equations
52. (Online) PDE Real Analysis Seminar, Graduate School of Mathematical Sciences, The University of Tokyo Oct 27, 2021
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    Vanishing discount problems for Hamilton–Jacobi equations on changing domains
53. Analysis Seminar, University of North Carolina at Charlotte Sep 17, 2021
    Remarks on rate of vanishing viscosity for Hamilton–Jacobi equations
54. PDE and Geometric Analysis seminar, University of Wisconsin – Madison Sep 30, 2019
    State-constraint static Hamilton–Jacobi equation in nested domains
55. Mathematical conference: Summer meeting 2019, University of Science, VNU-HCMC Jul 28, 2019
    State-constraint static Hamilton–Jacobi equation in nested domains

Contributed Talks & Presentation

• Boston-Keio-Tsinghua Workshop 2024: May 31, 2024
  slides   ·   schedule   ·   web
  Differential Equations, Dynamical Systems and Applied Mathematics, Boston University
  Rate of convergence for quasi-periodic homogenization of Hamilton–Jacobi equation and application

• 88th Midwest PDE seminar, The Ohio State University Apr 26, 2024
  pdf   ·   poster   ·   schedule   ·   web
  Properties of the effective Hamiltonian and homogenization of the Hamilton-Jacobi equation

• 8th OISS Annual Scholar Showcase Apr 05, 2024
  poster
  Office of International Students and Scholars, Michigan State Univeristy
  On the regularity of stochastic effective Hamiltonian

• Concentration week on Geometry and Analysis, Texas A&M University Jul 27, 2022
  web
  Remarks on rate of vanishing viscosity for Hamilton–Jacobi equations

• Physical Applied Math seminar, University of Wisconsin - Madison Sep 23, 2021
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  From Stochastic Optimal control to Deterministic Optimal control: rate of convergence of the value functions

• Geometric and Harmonic Analysis 2019, University of Connecticut Mar 30, 2019
  web
  Some recent works on homogenization of Hamilton-Jacobi equations

• CNA Workshop 2019: Mathematical Models for Pattern fomation, Carnegie Mellon University Mar 03, 2019
  poster   ·   web
  Homogenization of Hamilton-Jacobi equation: Rate of convergence

Research visits

• (2024-07) University of Seoul, Seoul, Korea, hosted by Dohuyn Kwon
• (2023-08) Academy of Mathematics and Systems Science, Chinese Academy of Science, BeijingChina, hosted by Jianlu Zhang
• (2023-11) North Carolina State University, USA, hosted by Khai T. Nguyen
• (2021-09) University of North Carolina - Charlotte, USA, hosted by Loc Nguyen

Selected Conferences, Workshops, and Summer Schools attended

1. (Withdrawn) Workshop: Recent progress in Hamilton-Jacobi equations and related topics Jun 02–06, 2025
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   Nanjing, China
2. Integro-differential equations in many-particle interacting systems Apr 14–18, 2025
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   American Institute of Mathematics, Pasadena, California
3. AMS Spring 2025 Central Sectional Meeting, University of Kansas, Lawrence Mar 29–30, 2025
   Frontiers in Nonlinear PDEs and Applied Mathematical Challenges
4. AMS Joint Math Meeting 2025 Jan 08–11, 2025
   
   Seattle, USA  ·  web
5. Brin Summer school: PDE and Randomness, University of Maryland Aug 01–06, 2024
   
   Maryland, USA  ·  poster  ·  schedule  ·  web
6. SIAM Great Lakes 2023 Meeting, Michigan State University Oct 15, 2024
7. Madison PDEs Conference, University of Wisconsin–Madison May 21, 2023
8. Concentration week on Geometry and Analysis, Texas A&M University July 29, 2022
9. (Online) The Twenty-Third Riviere-Fabes Symposium on Analysis and PDE April 28, 2021
10. (Online) High Dimensional Hamilton-Jacobi PDEs Stochastic PDEs, IPAM, UCLA May 01, 2020
11. High Dimensional Hamilton-Jacobi PDEs Tutorial, IPAM, UCLA Mar 01, 2020
12. AMS Fall Central Sectional Meeting, University of Wisconsin–Madison Sep 21, 2019
13. Mathematics conference: Summer meeting, University of Science, VNU-HCMC July 28, 2019
14. Geometric and Harmonic Analysis 2019, University of Connecticut Mar 03, 2019
15. CNA Workshop 2019: Mathematical Models for Pattern Formation, Carnegie Mellon University Mar 17, 2019
16. 81st Midwest PDE seminar, University of Wisconsin–Madison Apr 17, 2018
17. Fourth Chicago Summer School in Analysis, University of Chicago Jun 15, 2017
18. Minischool in Calculus of Variations and Nonlinear PDE, UC Berkeley May 15, 2017
19. Madison workshop in Analysis and PDEs, University of Wisconsin–Madison Oct 15, 2017
20. DAAD Spring School on Combinatorial Stochastic Processes, VIASM Mar 15, 2016
21. Summer Program on PDEs and Applied Mathematics, VIASM July 15, 2014

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