Isogeny-based group actions in cryptography

The hardness of computing discrete logarithms in a prime order group builds the basis of many constructions in cryptography.
While there exist efficient quantum algorithms for solving this problem, the situation is different when we consider group actions:
Given two elements $x,y$ in a set $X$, and a group $G$ acting on $X$, the "group-action DLOG problem" asks to find a group element $g \in G$ so that $y = gx$ (if it exists).

In this talk, the focus will be on group actions that are used in isogeny-based cryptography.
In particular, we will discuss different properties that are specific to the group action used in the Commutative Supersingular Isogeny Diffie-Hellman protocol (CSIDH).