The Yang-Baxter equation: algebra, geometry and mathematical physics

In the last 30 years there has been a particularly active interaction between mathematics and theoretical physics. Thanks to this interaction, new mathematical fields have emerged, which in turn provide new methods for various areas of theoretical physics.
The theory of the Yang-Baxter equation is one example of such areas. Solutions of this equation have a rich and deep mathematical structure and have numerous applications in physics. The lecture will give an overview of classical results and new developments in the theory of the Yang-Baxter equation.