Quanjun Lang

Quanjun Lang is an Assistant Research Professor of Mathematics at Duke University's Trinity College of Arts & Sciences since 2023. He holds a Ph.D. from Johns Hopkins University (2023). His research focuses on quantum information theory, applied mathematics, and statistical mechanics, particularly in kernel learning for operators, interacting particle systems, and non-Markovian dynamics. Lang teaches courses in probability (MATH 230/STA 230) and differential equations (MATH 353/753), emphasizing foundational mathematical concepts. His recent work includes developing methods for quantum channel learning and memory kernel estimation in generalized Langevin equations.

Research Interests: Lang's work bridges theoretical mathematics and applied sciences, addressing challenges in inverse problems and data-driven modeling. Key areas include:

• Quantum system characterization via low-rank matrix sensing
• Nonparametric estimation of interaction kernels in particle systems
• Regularization techniques for stochastic processes

Teaching: Recent courses include Probability (Fall 2023-2024), Ordinary and Partial Differential Equations (Spring 2025), and graduate-level Probability (Spring 2024). These reflect his expertise in stochastic processes and mathematical analysis.

Research Trends: His publications (2020–2025) demonstrate progression from foundational work on Dirichlet spaces to cutting-edge quantum information applications, showcasing interdisciplinary impact. Current trends focus on unifying measurement design with machine learning for complex dynamical systems.