The Selberg integral is a beautiful multidimensional analogue of Euler's beta integral first evaluated by Selberg in 1941/1944. After a period of obscurity Selberg's integral has since played important roles in analytic number theory, random matrix theory, enumerative combinatorics and conformal field theory. In their recent verification of the SU(2) AGT conjecture, a deep conjecture relating fundamental objects in conformal field theory, Alba, Fateev, Litvinov and Tarnopolskiy (AFLT) evaluated a new generalised Selberg integral which included a pair of Jack polynomials in the integrand. I will discuss different ways of evaluating the AFLT integral, and how these techniques give rise to elliptic and q-analogues, as well as higher-rank (SU(n)) integrals.

### 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 or Travis Scrimshaw.