We build rigorous theory and practical algorithms for electronic-structure calculations at the boundary of mathematics, chemistry, physics, materials science, and high-performance computing.
“The purpose of computing is insight, not numbers.” Richard Hamming
The fermionic many-body problem is mathematically well formulated but computationally formidable. Its exponential complexity demands approximations that are both sophisticated enough for real systems and structured enough to analyze.
We translate modern quantum-chemistry methods into precise mathematical frameworks. Numerical analysis, differential geometry, and algebraic geometry help explain convergence, approximation quality, and the structure of nonlinear equations.
We study physical systems near the limits of computational complexity and design algorithms that move those limits. Our work emphasizes robust solvers, reduced complexity, and reproducible implementations.
We connect classical high-accuracy methods with quantum algorithms and emerging hardware, looking for principled ways to study molecules and quantum materials through high-dimensional eigenvalue problems.
Each direction combines mathematical structure, algorithmic design, and applications to chemically or physically relevant systems.
Coupled-cluster theory is among the most successful high-accuracy wavefunction methods in computational chemistry. Its nonlinear parameterization makes calculations remarkably effective, but also raises deep questions about solvability, convergence, truncation, and error control.
Our group studies coupled-cluster equations through numerical analysis and nonlinear algebra. We develop diagnostics, robust solution strategies, low-scaling formulations, and geometric descriptions for reliable calculations in chemistry and materials science.
Quantum embedding methods divide a complex system into an active region, where strong correlation demands a high-level description, and an environment that can be treated more economically. This multiscale idea offers a path toward accurate calculations for larger molecules and materials.
We analyze density-matrix embedding theory and coupled-cluster-based static embedding, with particular attention to representability, self-consistency, optimization on matrix manifolds, and scalable environment solvers.
Quantum computers process high-dimensional information in fundamentally new ways, but useful quantum simulation requires much more than translating a classical formula into a circuit. Conditioning, measurement cost, state preparation, and hardware noise all shape what is computationally meaningful.
Our work develops mathematical and numerical foundations for quantum linear algebra and electronic-structure algorithms, connecting theoretical complexity with experiments on contemporary hardware.
Our publications span rigorous analysis, new algorithms, quantum embedding, coupled-cluster theory, and quantum simulation.