Seung-Yeon Ryoo

I am no longer associated with Princeton University, after having received my Ph.D. under the supervision of Professor Assaf Naor. Please visit my new webpage. I am now a postdoctoral teaching fellow at the Division of Physics, Mathematics and Astronomy of the California Institute of Technology.

My CV: pdf.

Research Interests.

• Metric geometry of nilpotent Lie groups, especially Carnot groups.
• Bilipschitz and snowflake embeddings of metric spaces into Euclidean and L^p spaces.
• Rigorous approaches to mathematical models of synchronization, with an emphasis on the Winfree and Kuramoto models.

Publications and Preprints.

1. Quantitative relaxation dynamics from generic initial configurations in the Kuramoto model (with Hangjun Cho, Jiu-Gang Dong, and Seung-Yeal Ha). arXiv Preprint
2. Asymptotics of Riemannian Lie groups with nilpotency step 2 (with Enrico Le Donne, Luca Nalon, Sebastiano Nicolussi Golo). arXiv Preprint
3. Vertical versus horizontal Poincaré inequalities on simply connected nilpotent Lie groups and groups of polynomial growth arXiv Preprint
4. Asymptotic formation and orbital stability of phase-locked states in Kuramoto–Lohe type synchronization models on Lie groups To appear in Commun. Math. Sci. arXiv Preprint
5. On the sharpness of the Assouad embedding theorem for finitely generated groups of polynomial growth and nilpotent Lie groups Doctoral disseration at Princeton University. (2023) Proquest link
6. Embedding snowflakes of Carnot groups into bounded dimensional Euclidean spaces with optimal distortion Analysis & PDE. 15-8, 1933-1990 (2022) arXiv
7. Constants of motion for the Lohe model with frustration and its applications to emergent dynamics (with Seung-Yeal Ha, Dohyun Kim, Hansol Park). Physica D: Nonlinear Phenomena. 416, 132781 (2021) arXiv
8. Asymptotic phase-locking dynamics and critical coupling strength for the Kuramoto model (with Seung-Yeal Ha). Commun. Math. Phys. 377, 811-857 (2020) arXiv
9. On the relaxation dynamics of Lohe oscillators on some Riemannian manifolds (with Seung-Yeal Ha, Dongnam Ko). J. Stat. Phys. 172, 1427-1478 (2018)
10. Emergence of partial locking states from the ensemble of Winfree oscillators (with Seung-Yeal Ha, Dongnam Ko, Jinyeong Park). Quart. Appl. Math. 75, 39-68 (2017)
11. Emergent dynamics of a generalized Lohe model on some class of Lie groups (with Seung-Yeal Ha, Dongnam Ko). J. Stat. Phys. 168, 171-207 (2017)
12. On the finiteness of collisions and phase-locked states for the Kuramoto model (with Seung-Yeal Ha, Hwa Kil Kim). J. Stat. Phys. 163, 1394-1424 (2016)
13. Emergence of phase-locked states for the Kuramoto model in a large coupling regime (with Seung-Yeal Ha, Hwa Kil Kim). Commun. Math. Sci. 14, 1073-1091 (2016)
14. On the emergence and orbital stability of phase-locked states for the Lohe model (with Seung-Yeal Ha). J. Stat. Phys. 163, 411-439 (2016)
15. Emergent dynamics of Winfree oscillators on locally coupled networks (with Seung-Yeal Ha, Dongnam Ko, Jinyeong Park). J. Differential Equations 260, 4203-4236 (2016)
16. Emergence of phase-locked states for the Winfree model in a large coupling regime (with Seung-Yeal Ha, Jinyeong Park), Discrete and Continuous Dynamical Systems 35, 3417-3436 (2015)

I have previously used the name Sang Woo Ryoo. Publications 1-10 were initially published under this name.