Asymptotics and lower bounds for complex and real counts of singular surfaces in $\mathbb{P}^3$

We use tropical geometry and floor decomposed tropical surfaces to study the asymptotics of counts of singular surfaces in $\mathbb{P}^3$ satisfying point conditions. In the real case, we give a lower bound for the number of real singular surfaces satisfying point conditions. This is joint work with Thomas Markwig, Kristin Shaw, Eugenii Shustin.