Nan Sheng

Researcher in mathematical and computational science
Ph.D. candidate, Computational Mathematics
Institute for Computational and Mathematical Engineering
Stanford University

Email: nansheng@stanford.edu
CV / Google Scholar / GitHub / LinkedIn

About

I am a Ph.D. candidate in Computational Mathematics at Stanford University. I am broadly interested in mathematical and computational structures underlying physical, chemical, and engineered systems.

My work concerns the mathematical and computational foundations of many-body theory, with applications to electronic structure, materials, molecular systems, quantum simulation, and scientific machine learning.

Before Stanford, I received a Ph.D. in Chemical Physics from the University of Chicago and B.S. degrees in Physics and Chemistry from the University of Chinese Academy of Sciences.

Recent focus

Exact density-functional theory, convex duality, and variational principles
Inverse Kohn–Sham theory, exchange-correlation functionals, and response theory
Quantum many-body methods, Green's functions, and embedding methods
Scientific computing, tensor methods, and AI for molecular/materials science

Selected papers

Foundational theory

Exact density-functional theory as parallel ensemble variational hierarchies: from Lieb's formulation to Kohn–Sham theory.
Nan Sheng. arXiv:2603.23399, 2026. [arXiv]

A unified variational framework for the inverse Kohn–Sham problem.
Nan Sheng. arXiv:2603.23452, 2026. [arXiv]

A density-functional perspective on force fields.
Nan Sheng. arXiv:2604.25215, 2026. [arXiv]

Computational many-body methods and scientific computing

Approximation of high-dimensional Gibbs distributions with functional hierarchical tensors.
Nan Sheng, Xun Tang, Haoxuan Chen, and Lexing Ying. arXiv:2501.17143, 2025. [arXiv]

Low-rank Green's function representations applied to dynamical mean-field theory.
Nan Sheng, Alexander Hampel, Sophie Beck, Olivier Parcollet, Nils Wentzell, Jason Kaye, and Kun Chen. Physical Review B 107, 245123, 2023.

Green's function formulation of quantum defect embedding theory.
Nan Sheng, Christian Vorwerk, Marco Govoni, and Giulia Galli. Journal of Chemical Theory and Computation 18, 3512--3522, 2022.

See the papers page for a complete list.