Structure of singularities for semicalibrated currents

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Semicalibrated currents are a generalization of calibrated submanifolds and appear naturally in various geometric problems, since the property of being merely semicalibrated is significantly easier to preserve under deformations. Semicalibrated currents are expected to share the regularity properties of area-minimizing currents, and indeed Almgren's celebrated dimension estimate on the interior singular set was shown to also hold for semicalibrated surfaces by Spolaor in 2015. I will talk about joint work with Paul Minter, Anna Skorobogatova, and Luca Spolaor, in which we build on this to establish a sharp structural result (rectifiability) for the interior singular set.

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