Holonomicity for skein modules of 3-manifolds with boundary

In this talk I will explain a recent result we obtained with Iordanis Romaidis which asserts that Kauffman bracket skein modules of 3-manifolds are finitely-generated and holonomic as modules for the skein algebras of the boundary surfaces. This immediately implies a long-standing conjecture of Frohman, Gelca and Lofaro concerning the annihilator of the empty skein, and it gives a new proof (after Garoufalidis-Le) that the quantum A-polynomial of a knot is holonomic.

The approach is largely that of geometric representation theory — we develop a non-abelian analog of the holonomicity framework of Sabbah in the quantum torus, which itself echoes Bernstein and Kashiwara's approach to holonomicity for ordinary differential equations.

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