Rational functions on semisimple Lie algebras and the Gelfand–Kirillov conjecture

The talk is aimed at describing recent solution of the rationality problem for fields of rational functions on semisimple Lie algebras and the intimately related construction of counterexamples to the Gelfand–Kirillov conjecture on the fields of fractions of universal enveloping algebras of semimple Lie algebras.