I have received my Ph.D. at Princeton University under the supervision of Professor Assaf Naor and am now a postdoctoral teaching fellow at the California Institute of Technology.
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.
On oscillator death in the Winfree model
Forthcoming manuscript.
Asymptotic phase-locking of the inertial Kuramoto model in the large coupling and small inertia regime (with Hangjun Cho, Jiu-Gang Dong, Seung-Yeal Ha).
Forthcoming manuscript.
Vertical versus horizontal Poincaré inequalities on simply connected nilpotent Lie groups and groups of polynomial growth Submitted.
arXiv Preprint
Asymptotic formation and orbital stability of phase-locked states in Kuramoto–Lohe type synchronization models on Lie groups Submitted.
arXiv Preprint
Embedding snowflakes of Carnot groups into bounded dimensional Euclidean spaces with optimal distortion
Analysis & PDE. 15-8, 1933-1990 (2022) arXiv
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
Asymptotic phase-locking dynamics and critical coupling strength for the Kuramoto model
(with Seung-Yeal Ha). Commun. Math. Phys. 377, 811-857 (2020) arXiv
On the relaxation dynamics of Lohe oscillators on some Riemannian manifolds
(with Seung-Yeal Ha, Dongnam Ko). J. Stat. Phys. 172, 1427-1478 (2018)
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)
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)
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)
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)
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)
Emergent dynamics of Winfree oscillators on locally coupled networks
(with Seung-Yeal Ha, Dongnam Ko, Jinyeong Park). J. Differential Equations 260, 4203-4236 (2016)
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)
NB. Publications 1-10 were initially published under my previous name "Sang Woo Ryoo".