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Speaker: David Jordan (​University of Edinburgh).

Skein modules are vector spaces attached to closed 3-manifolds and reductive groups G, which capture the calculus of line operators in Chern-Simons theory.  A few years ago we showed with Gunningham and Safronov that skein modules are finite-dimensional when the quantum parameter q is generic.  In this talk I will give a overview of recent progress since then:  I will survey the known formulas for 3-manifolds, I will explain finiteness for 3-manifolds with boundary, and with embedded line defects, and I'll also explain a new kind of finiteness result for skein categories.