Hanbaek Lyu

Hanbaek Lyu is an Assistant Professor in the Department of Mathematics at the University of Wisconsin-Madison, with an affiliation in the Department of Computer Science and membership in the Institute for Foundations of Data Science. His research spans discrete probability, matrix factorization, and machine learning, focusing on large discrete systems including interacting particle systems, networks, and structured random matrices.

His educational background includes:

• Ph.D. in Mathematics, The Ohio State University (2018); Thesis: "Combinatorial and probabilistic aspects of coupled oscillators" (Advisor: David Sivakoff)
• B.S. in Mathematics, Seoul National University

Lyu's research bridges theoretical probability and practical machine learning, with emphasis on optimization for dependent data and complex systems. His work develops foundational algorithms for matrix/tensor factorization while exploring synchronization phenomena in oscillator networks and phase transitions in particle systems. Recent publications highlight interpretable models for biological data and rigorous convergence guarantees for nonconvex optimization.

Analysis of his 15 most recent publications reveals three dominant threads: (1) optimization theory for constrained nonconvex problems applied to dictionary learning, (2) interacting particle systems and random matrix theory with combinatorial aspects, and (3) interpretable latent models for network dynamics and genomics. His work consistently combines probabilistic methods with computational applications.

Lyu leads two active NSF grants:

• DMS-2206296 (2022-2025): "Online Dictionary Learning for Dependent and Multimodal Data Samples: Convergence, Complexity, and Applications"
• DMS-2010035 (2020-2023): "Combinatorial and Probabilistic Approaches to Oscillator and Clock Synchronization"

He currently mentors five doctoral students across Mathematics and Computer Science departments, organizes UW-Madison's probability seminar, and collaborates with over 30 researchers including Janko Gravner, Lionel Levine, and Wenpin Tang on interdisciplinary projects spanning genomics, network science, and statistical physics.