University of Sydney Algebra Seminar

Yaping Yang (University of Melbourne)

Friday 27 April, 12-1pm, Place: Carslaw 375

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 $\mathrm{\Omega }$-background.