IMSc Webinar

Generalizations of the Selberg integral and combinatorial connections

Krishnan Rajkumar

Jawaharlal Nehru University

Webinar link: us02web.zoom.us/meeting/86959141402

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.