Abstract

My research is motivated by a question arising in first-principles calculations and dynamical mean-field theory: how can we represent and compute Green's functions and response functions efficiently without losing the underlying physics? This challenge becomes particularly acute in strongly correlated systems at low temperatures, in two-particle quantities, and in nonequilibrium dynamics.

This research grew out of materials studies of correlated electron systems, including pyrochlore oxides and LiV2O4, together with the development of practical tools for DFT+DMFT and quantum Monte Carlo. These efforts led to the intermediate representation (IR) basis, which provides a compact and system-independent description of imaginary-time Green's functions, and more recently to quantics tensor train (QTT) representations and tensor cross interpolation (TCI), which extend these ideas beyond imaginary time and provide a scalable route to multiscale structure in two-particle and nonequilibrium problems.

A central aspect of my work is that methods become most useful when embedded in shared software and a collaborative community. This perspective has driven the development of open-source ecosystems such as sparse-ir and DCore, as well as broader community-building efforts including tensor4all, workshops, schools, and hackathons.

At HKUST, I hope to build a research program at the interface of condensed matter theory, applied mathematics, and scientific computing, developing compact and scalable methods for quantum many-body problems through open-source software, AI-assisted development, and broad collaborations.