solvable many-body problems (quantal and classical), nonlinear evolution equations, isochronous models and zeros of polynomials

This paper is a report on the series of 3 lectures given at the 6th workshop and seminar on topics in theoretical physics (ttp6) held on september 19-21, 2019 at the azarbaijan shaid madani university in tabriz, iran. it starts with a terse synthesis of the talk i gave at the march meeting of the american physical society on the occasion of the award of the 2019 dannie heineman prize for mathematical physics. it then consist of an overview of past---and especially recent---findings on “exactly solvable” dynamical systems; focusing on the topics mentioned in the title of these series of 3 lectures.