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I will introduce a categorification of the theory of BPS invariants for a quiver with potential, or more generally, the category of coherent sheaves on a Calabi-Yau threefold. Via a perverse filtration on vanishing cycle cohomology, there is a Lie algebra whose graded dimension recovers the BPS invariants. This is joint work with Sven Meinhardt.

For a particular class of quivers with potential, this conjecturally recovers the Lie algebra inside the Yangian defined by Maulik and Okounkov, and produces a large new class of natural Borcherds algebras.