Title: A Free Boundary Problem for the Parabolic Poisson Kernel

Abstract: We study a free boundary problem for caloric measure first
introduced by Hofmann, Lewis and Nyström. In particular, we show that
the oscillation of the Poisson kernel of a domain controls the
oscillation of the unit space normal to that domain
(this is the parabolic analogue of Kenig and Toro's work on
harmonic measure). The key step is classifying "flat blowups." To
do so, we adapt the work of Andersson and Weiss on solutions
to a parabolic problem arising in combustion.