讲座内容：

The Selberg integral, an n-dimensional generalization of the Euler beta integral, plays a central role in random matrix theory, Calogero--Sutherland quantum many body systems, Knizhnik--Zamolodchikov equations, and multivariable orthogonal polynomial theory. In 1998, Baker and Forrester conjectured a q-analogue p+1 components generalization of the Selberg integral. Meanwhile, they formulated an equivalent constant term identity conjecture. The p=1 case of the identity was proved by K\'{a}rolyi, Nagy, Petrov and V. Volkov in 2015. In this talk, we show how the general p+1 components q-Baker--Forrester conjecture was proved.