Asymptotic behavior of the heat equation in free space
I always appreciate self-contained efforts to summarize thinking on basic topics. In contrast to textbooks, which by necessity need to address a broad set of techniques, a deep dive on one familiar topic can reveal the strengths and weaknesses of various mathematical perspectives.
Bayesian consistency, or (again) lack thereof
In applied math, the model is almost always mis-specified, and so we have to ask “if the truth is complicated and I apply Bayesian procedures to my simplified model, what kind of mistakes am I likely (or not likely) to make?”
Wilks’ phenomenon, or lack thereof
I commonly find myself in a situation where I want to decide whether or not a certain mechanism is present in an applied problem.