Branes, quantum toroidal algebras and R-matrices

I will review the correspondence between configurations of branes of Type IIB string theory and representation theory of quantum toroidal algebras. In particular I will show that the R-matrices of these complicated algebras arise from brane crossings similarly to how R-matrices of finite quantum groups arise in Chern-Simons theory from crossings of the Wilson lines. Time permitting, I will also present some applications to supersymmetric gauge theories in various dimensions.