What are K-3 surfaces? Some of you, maybe most, may have heard the term. Why did Andre Weil give them such a funny name (K-3?). What are they good for, why are they considered so important? Is it really true that whenever the number 24 comes up in mathematics, there is a K-3 surface lurking somewhere behind? Some geometers may consider them the most interesting surfaces of them all.
The talk will give a survey with many asides, and talk about individual K-3 surfaces, as well as their "sociology". It will explore connections with elliptic curves and Abelian surfaces, and many other things.