Krishnan Rajkumar: Generalizations of the Selberg integral and combinatorial connections
Channel: Amritanshu Prasad
Date: 2020-09-13

We'll briefly recall the history of the Selberg Integral and several variants. We'll also go through the proof of some of them like Aomoto's integral before focusing on known and possibly new integrals involving Schur polynomials and Jack polynomials. We shall note the implications that these integrals seem to count (after a suitable normalization) the number of standard young tableaux of skew shapes, before conjecturing the existence of several Naruse-type hook length formulas. Finally we will explain how these integrals arise in number theoretic problems.