Sam Adriaensen (Vrije Universiteit Brussel): The expander mixing lemma: Old wine in new bottles?

In counting problems in finite geometry, two simple yet powerful tools have played an important role. These techniques are often called the _standard equations_ and the _variance trick_. Often, the exact same results can be proved by applying a tool from spectral graph theory: the _expander mixing lemma_. In this talk, we will compare the different techniques. We will explore situations in which they seem to be interchangeable, but also situations in which they seemingly complement each other.