Appears in collection : 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

This talk highlights some geometric aspects emerging from the study of SLE curves and CFT. As examples, we shall mention versions of the Loewner energy (the anticipated action functional of these canonical curve models, or more rigorously, the rate function in large deviations principles for the random curves), classification problems of covering maps with prescribed critical points, and the emergence of the Virasoro algebra (the symmetry algebra of CFTs) from complex deformations of boundaries of bordered Riemann surfaces (i.e., loops).