In this reading project I studied some interesting results in Riemannian geometry. Starting from the definition of Riemannian metric, geodesics and curvature this thesis covers deep results such as Gauss-Bonnet theorem, ...

The complexity of several systems is a confluence of the intricate structure of their interactions and the intrinsic dynamics of its constituent elements. Complex network framework can be used to study such systems ...

This thesis aims to serve as an excursion into the theories of homology, cohomology and characteristic classes, conventional tools used to study topological spaces and vector bundles with origins in Algebraic Topology. ...