Explore new applications of Reflection Equation Algebras in this 42-minute lecture by Dimitry Gurevich at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the treatment of REA as q-analogs of enveloping algebras U(gl(N)) and their similar representation categories. Discover three key applications: q-analog of Schur-Weyl duality, q-Capelli formula, and q-Frobenius formula. Follow the comprehensive syllabus covering topics such as power case, quantum analog, commutative and determinants, power sums, matrix representation, super situation, free tensor algebra, super dimension, multiplication table, reflection equation property, quantum derivative, and classical formula. Gain insights into advanced mathematical concepts and their quantum counterparts in this in-depth exploration of Reflection Equation Algebras.