Research

Overview

My research studies mathematical and computational structures in physical, chemical, and engineered systems, especially where rigorous mathematics, physical modeling, and computation meet.

Recent work

My recent work spans four connected directions.

• Variational electronic-structure theory. Density-functional theory and Kohn–Sham constructions from variational and convex-analytic viewpoints, including exact DFT, ensemble principles, inverse Kohn–Sham problems, exchange-correlation functionals, and response.
• Computational many-body methods. Green's functions, dynamical mean-field calculations, quantum embedding, quantum simulation, and reduced descriptions of correlated electronic systems.
• High-dimensional scientific computing. Numerical methods for high-dimensional scientific problems, emphasizing tensor representations and optimization of high-dimensional functions, with applications to physics and control.
• AI for science and molecular/materials modeling. Scientific machine learning and data-informed modeling for molecular and materials problems, including robust quantum-chemistry models, force-field perspectives, scientific coding agents, and physics-informed approximations.

Broader interests

Outside my current paper trail, I remain interested in statistics and generative modeling, high-performance computing, quantum computing, theoretical physics, materials science, semiconductors, devices, circuits, chips, and engineering systems more broadly.