Junhee Ryu

About me

Currently, I am a Research Fellow at Korea Institute for Advanced Study (KIAS).

I completed my Ph.D. in mathematics at Korea University in February 2023 under the supervision of Prof. Kyeong-hun Kim. After graduation, I held successive positions as a Postdoctoral Fellow and a Research Professor at Korea University from March 2023 to February 2025.

Employment

• Research Fellow, School of Mathematics, Korea Institute for Advanced Study, 2025.03~ (Mentor: Joonhyun La)

• Research Professor, Department of Mathematics, Korea University, 2024.03~2025.02 (Mentor: Kyeong-hun Kim)

• Post-Doctoral Fellow, Department of Mathematics, Korea University, 2023.03~2024.02 (Mentor: Kyeong-hun Kim)

Visiting Positions

• Visiting Scholar, Division of Applied Mathematics, Brown University, 2023.03~2024.06 (Hosted by Hongjie Dong)

Education

• Ph.D. in Mathematics, Korea University, 2017.03~2023.02 (Thesis Advisor: Kyeong-hun Kim)

• B.S. in Mathematics, Korea University, 2013.03~2016.08

Research Interests

• Deterministic and Stochastic Partial Differential Equations

• Space-time non-local equations on domains

• Non-local operators related to stochastic processes

• Degenerate equations

Preprints

1. (with K.-H. Kim) The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,\sigma}$ open sets [arXiv]

2. (with H. Dong) On nondivergence form linear parabolic and elliptic equations with degenerate coefficients [arXiv]

Publications

1. (with H. Dong) Sobolev estimates for parabolic and elliptic equations in divergence form with degenerate coefficients, to appear in Trans. Amer. Math. Soc. [arXiv]

2. (with K.-H. Kim) Weighted Sobolev space theory for non-local elliptic and parabolic equations with non-zero exterior condition on $C^{1,1}$ open sets, J. Evol. Equ. 25(60), 2025 [arXiv], [Journal]

3. (with H. Dong) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, SIAM J. Math. Anal. 56(4), 2024 [Arxiv], [Journal]

4. (with  K.-H. Kim and J.-H. Choi) Sobolev regularity theory for the non-local elliptic and parabolic equations on $C^{1,1}$ open sets, Discrete Contin. Dyn. Syst. 43(9), 2023 [Arxiv], [Journal]

5. (with K.-H. Kim and D. Park) A Sobolev space theory for the stochastic partial differential equations with space-time non-local operators, J. Evol. Equ. 22(57), 2022 [Arxiv], [Journal]

6. (with K.-H. Kim and D. Park) An $L_q (L_p)$-theory for diffusion equations with space-time nonlocal operators, J. Differ. Equ. 287, 2021 [Arxiv], [Journal]

Lecture Series

1. A Tutorial on Stochastic Partial Differential Equations (SPDEs), Probability Summer School in Korea 2025, June 22-26, 2025

Talks

1. (Invited) The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,\sigma}$ domains, POSTECH Probability Seminar, August 4, 2025

2. (Invited) Partial Differential Equations in Weighted Sobolev Spaces, KIAS APP Seminar, July 9, 2025

3. (Contributed) Sobolev estimates for SPDEs with nonlocal operators in domains, 2025 KMS Spring Meeting, April 24-26, 2025

4. (Invited) Sobolev estimates for SPDEs with nonlocal operators in domains, Probability Workshop in Korea 2025, January 19-22, 2025

5. (Invited)  Sobolev estimates for degenerate linear equations on the upper half space, 14th AIMS conference, December 16-20, 2024

6. (Invited) Sobolev estimates for degenerate linear equations on the upper half space, Workshop on Probability and PDEs, July 8-10, 2024

7. (Invited) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, KIAS APP Seminar, January 18, 2024

8. (Contributed) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, JMM 2024, January 3-6, 2024

9. (Invited) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, KAIST PDE Seminar, December 12, 2023

10. (Invited) A Sobolev space theory for SPDEs with space-time non-local operators, Cornell Probability Seminar, December 4, 2023

11. (Contributed) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, The 19th Prairie Analysis Seminar, November 3-4, 2023

12. (Invited) Sobolev regularity theory for non-local equations on $C^{1,1}$ open sets, Conference on Probability and PDEs, April 20-21, 2023

13. (Invited) Sobolev regularity theory for non-local equations on $C^{1,1}$ open sets, Brown PDE Seminar, April 7, 2023

14. (Contributed) Sobolev space theory for the Dirichlet problem of the elliptic and parabolic equations with the fractional Laplacian on $C^{1,1}$ open sets, 2022 KMS Spring Meeting, April 28-29, 2022

15. (Contributed) Deterministic and stochastic parabolic equations with space-time non-local operators, 2021 KMS Annual Meeting, September 20-21, 2021

16. (Contributed) A Sobolev space theory for SPDEs with space-time nonlocal operators, Bernoulli-IMS 10th World Congress in Probability and Statistics, July 19-23, 2021

17. (Contributed) A Sobolev space theory for SPDEs with space-time nonlocal operators, 2021 KMS Spring Meeting, April 29-30, 2021

Organized Seminars

1. Seick Kim: TBA, KIAS APP Seminar, November 7, 2025

2. Taekyu Kim: TBA, KIAS APP Seminar, September 24, 2025

3. Kihoon Seong: Central limit theorem for Φ^4 QFT measures in low temperature and thermodynamic limit, KIAS_APP Seminar, June 18, 2025

Grants

• New generation research program (PI), Korea Institute for Advanced Study, 2025.03~2027.02

Referee for

• Mathematische Annalen

• Calculus of Variations and Partial Differential Equations