This talk will briefly introduce free-boundary problems and some previous results about their structure. The main focus, however, will be on some recent results by Edelen and Engelstein which give dimension bounds on the singular strata of solutions to a broad class of free-boundary problems. The proof of these results centers around a complicated covering argument. The purpose of this talk is to introduce the major ideas and adumbrate the general argument. Some hands will get dirty. Friendships may be permanently altered. But, there will be cookies, so come and join in the fun.
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Fine Structure of the Free-Boundary, or "What is going on underneath the covers?"