Ziran Liu

My research is on both Mathematics and AI, spanning math for AI and AI for math. Mathematically, my work is rooted in probability theory and differential geometry, and these also remain the central topics to my work in pure mathematics. I move in both directions: I develop new mathematics for AI, and I apply mathematical structure into methods for solving problem in learning theory — while also exploring how AI can contribute back to mathematics. My projects always come as dual programs: a foundational mathematical line that is motivated by AI and a companion AI track to apply the developed mathematics.

Bio: I am currently a postdoctoral researcher at the Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS) and Research Institute of Intelligent Complex Systems, Fudan University. I received my Ph.D. in Operations Research (Honored, Beta Gamma Sigma) from NYU Stern. Before that, I received an M.S. in mathematics (probability theory) at NYU Courant, and an M.S. in mathematics (differential geometry) at Chern Institute of Mathematics at Nankai University. I graduated with B.S. in pure mathematics (Honored, Class of S. S. Chern) at Nankai University.

Acknowledgements: I am deeply grateful to my Ph.D. advisors and committee members — Paul Bourgade, Peter Lakner, Josh Reed, and S. R. S. Varadhan— for their guidance and support. I am especially indebted to Henry P. McKean (in memoriam), whose mentorship continues to shape my work.

Keywords of my recent papers: stochastic analysis, reflected diffusions, geometric structures in learning dynamics, reflected diffusion models, optimal transport, Dirac operator and spectral geometry, generative models, AI for mathematics, probabilistic structures in representation theory, rough paths, geometric deep learning, and stochastic dynamics of learning systems.

Upcoming Events

AI for Mathematics @SIMIS: I am organizing a SIMIS Colloquium and a workshop focusing on AI for pure mathematics, scheduled for April 6-7, 2026， at the Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS).