Quantum geometry, namely quantities such as quantum metric, Berry curvature, and Chern number, have become increasingly important in understanding interacting many-body systems. We have shown that supercurrents and superfluidity in a flat band are governed by quantum geometry [1], which opens new prospects for achieving high temperature superconductivity. These findings have become relevant for superconductivity in twisted bilayer graphene and other moiré materials [2]. We present our newest results on the topic, showing that flat band superconductivity is governed by the minimal quantum metric, which can be obtained by utilizing the system symmetries [3]. We discuss how effects unique to flat bands appear also in the normal state above the superconducting critical temperature [4,5]. Further, we show that quantum geometry governs the behaviour of bosonic condensates in flat bands as well, making quantum fluctuation effects remarkably strong [6].

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