I am an assistant professor in the Department of Mathematics at University of Wisconsin – Madison, and also a member of the Institute for Foundations of Data Science. I am also affiliated with the department of computer science at UW-Madison.

I work in the fields of probability, combinatorics, dynamical systems, optimization, and machine learning.

My research is broadly driven by questions related to understanding emergent or latent properties of complex systems and data sets. Such questions and techniques that I develop to address them span across the fields of probability, combinatorics, dynamical systems, optimization, and machine learning.

I am the principal investigator of the following grants:

- NSF Grant DMS-2206296 (2022-2025) on “
*Online Dictionary Learning for Dependent and Multimodal Data Samples: Convergence, Complexity, and Applications”;* - NSF Grant DMS-2010035 (2020-2023) on “
*Combinatorial and Probabilistic Approaches to Oscillator and Clock Synchronization”.*

NEW: I am serving as an Editorial Board member of *Scientific Reports.*

I am looking for self-motivated Ph.D students starting from Fall 2021. Please send me your CV to hlyu@math dot wisc dot edu.

Before joining UW-Madison, I was a Hedrick Assistant Professor at UCLA department of mathematics.

I earned a Ph.D in mathematics at the Ohio State University in 2018. My thesis is on “Combinatorial and probabilistic aspects of coupled oscillators“. David Sivakoff was my thesis advisor. (Slides for my dissertation talk: thesis_talk)

I earned my B.S. in mathematics at Seoul National University in South Korea.

- CV: CV_lyu
- Research Statement (5 pages): statement_Lyu

My collaborators are Janko Gravner, Lionel Levine, John Pike, Facudo Memoli, Matthew Junge, Eric Foxall, Michael Damron, Pasha Pylyavskyy, Arnab Sen, Tobias Johnson, Atsuo Kuniba, Masato Okado, Deanna Needell, Laura Balzano, Igor Pak, Sam Dittmer, Georg Menz,, Wenpin Tang, Joel Lewis, Sangchul Lee, Marek Biskup, Hanqin Cai, Yacoub Kureh, Chris Strohmeier, Mason Porter, Sumit Mukherjee, and Ahmet Alacaoclu.