Topology and correlation-driven symmetry breaking have long served as powerful frameworks for classifying phases of matter in crystals. These notions describe the microscopic behavior of quasiparticles and are manifested in macroscopic experimental observables. Recent advances in quantum geometry (QG) have sparked a renewed interest, revealing exciting connections between QG quantities—such as Berry curvature and quantum metric—and a range of electronic properties and experimental signatures in symmetry-breaking and topological phases in correlated systems. These insights have also underscored the interplay between QG and electronic correlations, positioning QG as both a diagnostic tool and a potential tuning mechanism for the realization of exotic correlated phases. The diverse array of QG quantities defined in momentum-, real-, and generalized spaces further calls for a systematic and in-depth investigation of their roles at the intersection of symmetry, topology, and correlation.

This KITP program aims to explore:

• Establishing mathematical and theoretical frameworks for quantum geometric quantities at both single-electron and many-body levels.
• Bridging the theoretical and experimental frontiers in QG, including identifying the experimental observables for generalized QG, discovering QG-rich materials platforms, and controlling QG via experimental knobs
• Understanding the role QG plays in correlated systems, symmetry-broken and topological phases, gapless systems, and more, in terms of a wide range of analytical and numerical methods.