**UM Math Graduate Students Seminar**

Armando Cabrera

* University of Miami *

**will present**

**A discrete version of the Gauss-Bonnet theorem **

Friday, April 19, 2013, 3:45pm

Ungar Building Room 402

**Abstract:**One of the deepest theorems in the differential geometry of surfaces is the Gauss-Bonnet theorem; it relates a geometric quantity, the Gaussian curvature, with a topological invariant, the Euler Characteristic. In this talk, we will review the definition of the Gaussian curvature of a smooth surface and define the corresponding concept for a (non-smooth) polyhedral surface. After this, we will be able to prove the Gauss-Bonnet theorem for such surfaces. This is closely related to Descartes' Elementary Treatise on Polyhedra, a work that remained unknown to the mathematical community for more than two hundred years.

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