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The pop-stack operator of a finite lattice $L$ is the map$\mathrm{pop}^{\downarrow}_L\colon L\to L$ that sends each element $x\in L$ tothe meet of $\{x\}\cup\text{cov}_L(x)$, where $\text{cov}_L(x)$ is the set ofelements covered by $x$ in $L$. We study several properties of the pop-stackoperator of $\mathrm{tors}\Lambda$, the lattice of torsion classes of a$\tau$-tilting finite algebra $\Lambda$ over a field $K$. We describe thepop-stack operator in terms of certain mutations of 2-term simple-mindedcollections. This allows us to describe preimages of a given torsion classunder the pop-stack operator.  We then specialize our attention to Cambrian lattices of a finite irreducibleCoxeter group $W$. Using tools from representation theory, we provide simpleCoxeter-theoretic and lattice-theoretic descriptions of the image of thepop-stack operator of a Cambrian lattice (which can be stated withoutrepresentation theory). When specialized to a bipartite Cambrian lattice oftype A, this result settles a conjecture of Choi and Sun. We also settle arelated enumerative conjecture of Defant and Williams. When $L$ is an arbitrarylattice quotient of the weak order on $W$, we prove that the maximum size of aforward orbit under the pop-stack operator of $L$ is at most the Coxeter numberof $W$; when $L$ is a Cambrian lattice, we provide an explicit construction toshow that this maximum forward orbit size is actually equal to the Coxeternumber.

Pop-Stack Operators for Torsion Classes and Cambrian Lattices