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Hall algebras and Fukaya categories

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HTLW04 - Quantum topology and categorified representation theory

(joint with Ben Cooper)

The multiplication in the Hall algebra of an abelian category is defined by “counting extensions of objects,” and the representation theory of this algebra tends to be quite interesting (e.g. Ringel showed the Hall algebra of modules over a quiver is the quantum group). Recently, Burban and Schiffmann explicitly described the Hall algebra of coherent sheaves over an elliptic curve, and various authors have connected this algebra to symmetric functions, Hilbert schemes, torus knot homology, the Heisenberg category, and the skein algebra of the torus. Motivated by this last connection and homological mirror symmetry, we discuss some computations in progress involving the Hall algebra of the Fukaya category of a (topological) surface.

This talk is part of the Isaac Newton Institute Seminar Series series.

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