# Yaping Yang (University of Melbourne)

## Double current algebras and applications

The deformed double current algebra associated to a complex simple Lie algebra $$\mathfrak{g}$$ is defined by Guay recently as a rational degeneration of the quantum toroidal algebra of $$\mathfrak{g}$$. It deforms the universal central extension of the double current algebra $$\mathfrak{g}[u, v]$$. In my talk, I will introduce the deformed double current algebra and give two applications. The first is the elliptic Casimir connection constructed by Toledano Laredo and myself. It is a flat connection with logarithmic singularities on the elliptic configuration space. The second is the work of Kevin Costello on the AdS/CFT correspondence in the case of M2 branes in an $$\Omega$$-background.