The deformed double current algebra associated to a complex simple Lie algebra g is defined by Guay recently as a rational degeneration of the quantum toroidal algebra of g. It deforms the universal central extension of the double current algebra 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.

### About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 3pm to 3.50pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

#### Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

Contact us

To volunteer to talk or to suggest a speaker, email Ole Warnaar.