A pointwise ergodic theorem for the action of a countable group $\Gamma$ on a probability space equates the global ergodicity of the action to its pointwise combinatorics. Our main result is a short, combinatorial proof of the pointwise ergodic theorem for actions of amenable groups along Tempelman F{\o}lner sequences, which is a slightly less general version of Lindenstrauss's celebrated theorem. We will discuss a very short proof (due to Tserunyan) of Birkhoff's classical pointwise ergodic theorem, and, using this proof as an outline, we will sketch the proof of the theorem for Tempelman F{\o}lner sequences. This is joint work with Jon Boretsky.
