I am interested in interacting particles systems analyzed through nonlinear partial differential equations (PDE) and probability theory. My goal is to deepen our understanding of the interplay between nonlinear interactions and stochastic noise. This interplay gives rise to rich mathematical phenomena such as, phase transitions, propagation of chaos, the log-Sobolev inequality, and the stability of stationary solutions. I also explore statistics, optimization, and deep learning, seeking analytical problems.

1. KM, Matthew Rosenzweig,  Phase Transitions and Linear Stability for the Mean-Field Kuramoto-Daido model, in preparation, 2025

2.  Jaewoong Cho, Kartik Sreenivasan, Keon Lee, KM, Soheun Yi, Jeong-gwan Lee, Anna Lee, Jy-yong Sohn, Dimitris Papailiopoulosw, Kangwook Lee, Mini-Batch Optimization of Constrastive Learning, Transactions on Machine Learning Research, 2024, https://openreview.net/pdf?id=Nux7OVXpJ9

3. KM, Cutoff and Metastability for the homogeneous Block Mean-field Potts model, in preparation, 2023

(Fixing technical issues in the arxiv version: https://arxiv.org/abs/2211.11463 )

•  Summer School in Optimal Transport and Applications, University of California, Santa Barbara, USA. (scheduled in Jul. 2025)

•  Frontiers in Applied Analysis, Carnegie Mellon University, Pittsburgh, USA. (scheduled in Jun. 2025)

•  Workshop on Probability and Mathematical Physics in Gimhae, Gimhae, South Korea (Dec. 2024)

•  Stochastic PDEs in Seoul 2024, KIAS, Seoul, South Korea (Aug. 2024)

•  The 2024 Summer School on Random Matrices, University of Michigan, Ann Arbor, USA (Jun. 2024)