Balázs Patkós: Forbidden subposet problems for traces of set families

The trace of a family $\mathcal{F}$ on a set $T$ is $\{F\cap T: F\in\mathcal{F}\}$. In extremal porblems addressing traces of sets, extremal families are usually those consisting of the smallest/largest possible subsets. For forbidden subposet problems, (asymptotically) extremal families consist of sets of size as close to $n/2$ as possible with $n$ being the size of the underlying set. We consider problems that somehow bridge these two topics.
Joint work with Daniel Gerbner and Mate Vizer.