Abstract: During this talk, we introduce the definition of a conformal curve; a generalization of holomorphic functions/curves and conformal mappings. A conformal curve is a mapping satisfying a suitable Cauchy-Riemann equation involving a calibration (Harvey and Lawson '82). In a recent joint work with Pankka, we studied the class of calibrations for which every conformal curve factors as a composition of a Möbius transformation and an affine isometry. We proved that the class is a dense G_delta -subset of all calibrations. Thus, a conformal curve that is not such a composition is necessarily related to an exceptional calibration. In this talk, we cover an example of such a conformal curve.
