My focus lies within condensed matter theory, particularly emphasizing novel topological and geometrical aspects of strongly correlated systems and topological phases of matter. My primary research revolves around unraveling the collective behavior of electrons in the fractional quantum Hall (FQH) effect. Notably, I proposed an effective field theory of gravitons in various fractional quantum Hall states and introduced an experimental setup that successfully verified the presence of gravitons in the Laughlin state. In recent endeavors, I studied vortex crystals in a rotating superfluid, employing fracton-elastic duality and non-commutative field theory. My exploration encompassed quantum melting scenarios and the fractonic nature of topological excitations. Additionally, I applied symmetric tensor gauge theory to analyze skyrmion systems in ferromagnets. Employing higher-form symmetry, I analyzed topological phase transitions in lattice quantum models. Expanding my research scope, I delved into the electromagnetism of twisted materials using effective theory formalism.