In these three talks I will introduce the notion of a vertex operator algebra V (a VOA for short), and two algebras associated to V (the Poisson algebra and the Zhu algebra). I plan to illustrate these concepts with examples. In the first talk, these will include affine VOAs and VOAs associated to a rank one lattice (both root lattices and non root lattices). In the second talk, I will compare and contrast two very different important families of W-algebras, which can be defined in terms of generators and relations or interpreted as kernels of operators acting on the Lattice VOAs from the first talk. The talks will be basic (short on technical details, long on bigger picture) aimed at graduate students or postdocs (or even faculty), so we can have some basic language in common. It is fine to come to the second talk if you miss the first one.

* *