Abstract: I this talk we will derive the first black hole solution to the Einstein field equations as was done by Karl Schwarzschild in 1915. We will discuss the strange properties of this spacetime with the help of new coordinate systems, Killing vectors, and Penrose diagrams. We will then present the Birkhoff and uniqueness theorems which tell us there are only four different black hole solutions in 4 dimensions. If time permits we will quickly review the casual structure of these other spacetimes.

The only thing I will be assuming for the talk is that everyone is reasonably familiar with differential geometry.

Abstract: The theory of framed motives developed by Garkusha and Panin based on ideas by Voevodsky, gives a tool to construct fibrant replacements of spectra in A^1-homotopy category. In the talk we will discuss how this construction gives an identification of the motivic homotopy groups of the base field with its Milnor-Witt K-theory. In fact, this identification can be done in the same manner as the theorem of Suslin-Voevodsky which identifies motivic cohomology of the base field with Milnor K-theory.