Speaker: Yijia Chen Title: Some Remarks on Enumerating Homomorphisms. Abstract: Let $C$ be a class of structures. In the problem $ENUM(C)$ we are given two structures $A$ and $B$ with $A\in C$, the goal is to compute all homomorphisms from $A$ to $B$. The main question is to find conditions on $C$ which ensure tractable $ENUM(C)$. In this talk, I will explain our attempt towards a complexity classification of $ENUM(C)$, including its connection to ETH and a new tractable case. This is ongoing joint work with Hubie Chen.