Arithmetic Geometry is algebraic geometry with the goal of finding how the absolute Galois group of Q acts on geometric objects defining solutions to problems. In this particular seminar the geometric objects will be spaces that define solutions to several well-known problems, especially including the Inverse Galois problem. One example of those moduli spaces are the modular curves studied by Mazur, Wiles, and many others.
The introduction of these spaces requires some cohomology of finite groups. The first part of the talk may be well-known to those who have had some cohomology. Yet, the treatment is different. It will allow introducing groups and equations that put some of those famous problems in a new context.