turkmath.org

I will shortly review the quantum Yang-Baxter equation which plays a prominent role in modern mathematical physics, especially in conformal field theory, statistical mechanics, string theory, knot theory, combinatorics, topology, etc. Then I will present new solutions to the Yang-Baxter equation and discuss their properties. These new solutions are expressed in terms of hypergeometric integrals. If time permits I will discuss the role of the Yang-Baxter equation in different areas of mathematical physics.