The Loewner energy is a conformally-invariant functional of curves in the upper half plane H that has connections to hyperbolic geometry, SLE theory, Teichmuller theory and geometric function theory.  In this talk we study "one-point" minimizers of Loewner energy, asking what curves minimize the energy among all which pass through a given point in H, and what curves minimize the energy among all which weld given points x<0

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