## Course description

Vector bundles can be thought of as vector spaces parametrized by a base space, where “space” can mean a topological space, an algebraic variety, or a manifold. They occurence is abundant in topology, geometry, and algebra. Characteristic classes are cohomological invariants of vector bundles and the most important and powerful tools to study them.

This course is a PhD level course on characteristic classes in topology, algebra, and geometry, including an introduction to vector bundles, cohomology, and differential geometry.

## Course goals

The course goal is to understand and be able to apply the concept of characteristic classes in a range of mathematical disciplines. At the end of the course, the student will be able to follow current research literature and, if desired, pursue own research projects in this area.