Jae-Hwan Choi(최재환)

Resume

Employment

• Research Fellow, School of Mathematics, Korea Institute for Advanced Study, 2025.05 - (Mentor: Prof.  Joonhyun La) 

• Postdoctoral Researcher, Research Institute of Mathematics (Probability group), Seoul National University, 2024.09 - 2025.04 (Mentor: Prof. Sung-Soo Byun)

• BK Postdoctoral Researcher, Department of Mathematical Sciences, KAIST, 2022. 09 - 2024.08 (Mentor: Prof. Jaeyoung Byeon)

Education

• Ph.D. in Mathematics,  Korea University, 2016.9 ~ 2022.8 (Advisor: Prof. Kyeong-Hun Kim)

(Military service: Republic of Korea Marine Corps (Officer), 2014.3 ~ 2016.2)

• B.S. in Mathematics, Korea University, 2010.3 ~ 2014.2

Research Interests: Probability and Analysis

• Deterministic and Stochastic Partial Differential Equations; Well-posedness and optimal regularity of the solution

• Differential Operators; Pseudo-differential operators with restricted smoothness, Non-local operators related to stochastic processes

• Ordinary and Stochastic Differential Equations; DiPerna-Lions theory, Krylov type estimate

• Large Deviation Principle; Freidlin-Wentzell LDP

• Harmonic Analysis; Application to PDEs and SPDEs, e.g., Calderon-Zygmund theory, Littlewood-Paley theory, Multiplier theory, and Generalized stochastic process theory

• Mathematical Foundations of AI: Optimal transport theory and its applications in machine learning, Neural network approximation theory

Selected Publications

1. J.-H. Choi, J.B. Lee, J. Seo, K. Woo, On the trace theorem to Volterra type equations with local or non-local derivatives. Journal of Evolution Equations, Volume 26, Issue 1, Article number 42, 2026.  [arXiv link 45 pages, Journal link 60 pages]

2. J.-H. Choi, B.-S. Han, D. Park, Sobolev regularity theory for stochastic reaction-diffusion-advection equations with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions. Journal of Differential Equations, Volume 451, 113761, 2026. [arXiv link 55 pages, Journal link 79 pages, Research Highlight]

3. J.-H. Choi, A regularity theory for evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces. Potential Analysis, Volume 63, Issue 2, pages 557-577, 2025. [arXiv link 19 pages, Journal link 21 pages]

4. J.-H. Choi, J. Kang, D. Park, A regularity theory for parabolic equations with anisotropic non-local operators in Lq(Lp) spaces. SIAM Journal on Mathematical Analysis, Volume 56, No. 1, pages 1264-1299, 2024. [arXiv link 31 pages, Journal link 36 pages]

5.  J.-H. Choi, K.-H. Kim, J. Ryu, Sobolev regularity theory for the non-local elliptic and parabolic equations on C^{1,1} open sets. Discrete and Continuous Dynamical Systems, Volume 43, Issue 9, pages 3338-3377, 2023.  [arXiv link 42 pages, Journal link 40 pages]

Teaching

1. 2017 spring semester - 2022 spring semester, Teaching Fellow at Korea University (Certification)

• Course : Analysis (1,2,3), ODE, Probability and Statistics, Set theory, Linear Algebra 1.

Awards, Honors, Fellowships, and Grants

1. New generation research program grant (MG102701, Principal Investigator), May 2025 ~ April 2027

• Korea Institute for Advanced Study

2. Basic Research Grant (RS-2023-00252516, Participating Researcher), March 2025 ~ February 2026

• National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT

3. Stochastic Analysis & Application Research Center (2019R1A5A1028324, Participating Researcher), September 2024 ~  February 2026

• National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT

4. Creative Challenge Research Grant (RS-2023-00237315, Principal Investigator), June 2023 ~ April 2025

• National Research Foundation of Korea (NRF) funded by the Ministry of Education 

5. Miwon Du-Myeong Fellowship, May 2023

• Miwon Commercial Co., Ltd. & Department of Mathematical Sciences, KAIST

6. Graduated with Honors (Great Honor; Magna Cum Laude), February 2014

• Korea University

7. National Science and Engineering Scholarship, March 2010 ~ February 2014

• Korea Student Aid Foundation (KOSAF)