I'm interested in systems that have quasi-periodicity either spatially or temporally. In such systems, the lack of unit length or time scale prohibits defining crystal momentum and dispersion relation. Instead, it gives unique physical phenomena such as the multi-fractal spectrum and states. I study such unique physical phenomena using abstract mathematical concepts of the tiling space (e.g. pattern equivariant topology, gap labeling theorem).

My research interests also lie in quantum entanglement and quantum information theory, with a particular focus on understanding how complex quantum correlations emerge, evolve, and can be harnessed in many-body systems. I aim to explore both fundamental aspects and potential applications of entanglement in areas such as quantum computation, communication, and the study of novel quantum phases emergent in complex many-body systems. Particularly, I study the significance of quasiperiodicity in the quantum information science and long-range entanglement by exploring the scaling behaviors of entanglement measure.

I'm also interested in strongly correlated electron systems, where interactions between electrons play a central role in shaping the physical properties of matter. These systems exhibit rich and unconventional phenomena—such as Mott insulators, superconductivity, magnetism, and quantum spin liquids—that lie beyond the scope of traditional band theory. I aim to understand the emergent behavior in such systems and uncover new organizing principles of quantum matter driven by strong correlations under the quasiperiodic media.

More recently, I have also developed a strong interest in open quantum systems and non-Hermitian physics. These frameworks provide powerful tools to describe quantum systems interacting with their environments, revealing novel dynamical phases and non-equilibrium phenomena that do not appear in closed systems. I am particularly intrigued by how non-Hermitian effects can reshape the structure of quantum states and correlations, offering new perspectives on control and characterization of quantum matter.