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Résumé |
Geometry has shaped our understanding of the physical world since antiquity. In today’s quantum era,
advances in experimental probes are revealing a new notion of “shape” encoded in the wavefunctions of
quantum matter.
In this talk, I will show how topology and geometry provide powerful frameworks for characterizing
quantum materials and give rise to experimentally accessible signatures. First, I will discuss the topology
of metallic systems, where global properties of the Fermi sea define distinct phases, and present recent
developments demonstrating how quantized correlation and transport effects can probe this topology in
both solid-state and ultracold-atom platforms.
I will then discuss the notion of quantum geometry, which describes the local structure of electronic
wavefunctions, and show how charge fluctuations provide a versatile probe of the quantum metric in both
insulators and metals. Together, these results illustrate how the “quantum shape” of matter can be directly
accessed in experiments and connected to the information content of many-body systems, opening new
avenues for understanding and engineering quantum materials.
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