Conical symplectic resolutions are a rather loosely defined class of hyperkähler varieties arising from canonical constructions in representation theory. Important examples include hypertoric varieties, Nakajima quiver varieties and Hitchin spaces. I will talk about Fukaya categories of conical symplectic resolutions. These are very rich objects, and they also turn out to be related to geometric representation theory. I will try to give an overview of this circle of ideas (much of which is not new in the symplectic literature). Any new content discussed in this talk is joint work with (subsets of) Benjamin Gammage, Justin Hilburn, Christopher Kuo, David Nadler and Vivek Shende.

https://sites.google.com/view/kyoto-symplectic/