Student AG Seminar: Resolution of singularities

Most algebraic geometers regard Hironaka's resolution of singularities as an esoteric monolith, useful to be aware of and use as a black box but too complicated to justify learning how it actually works. In reality, the modern revised form of Hironaka's proof is surprisingly simple and conceptually elegant. Furthermore, the techniques used illustrate several fundamental principles of birational geometry in a relatively concrete setting, which makes it a great starting point for learning the modern theory. In this talk I will explain the core ideas of the proof, and hopefully be able to give you a fairly complete sketch of how it works.