Siarhei Finski

Gauss-Bonnet theorem states that the mean curvature of a real surface is related to its Euler characteristic. This theorem, hence, relates the geometry of the surface to its topology. By using Hodge theory, the theorem can be rephrased as a calculation of the index of a certain differential operator, which interprets the Gauss-Bonnet theorem as an instance of an index theorem. In this talk, I will explain the above interpretation and show some consequences of that point of view.