Quantum Toroidal and Shuffle Algebras, R-matrices and a Conjecture of Kuznetsov

In this paper, we prove that the quantum toroidal algebra of type A is isomorphic to the double shuffle algebra of Feigin and Odesskii. The shuffle algebra viewpoint will allow us to prove a factorization formula for the universal R-matrix of the quantum toroidal algebra, and also prove a conjecture of Kuznetsov about the K-theory of affine Laumon spaces

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Refined knot invariants and Hilbert schemes

Moduli of Flags of Sheaves and their K-theory