Parabolic Uniform Rectifiability: A Survey

Resumen:

In this talk we will introduce the theory of Uniform Rectifiability (UR), in the setting
of parabolic geometry. Our approach will be through a historical overview of the classical
theory of rectifiability and UR in the euclidean setting. We will emphasize the interactions of
these theories with Harmonic Analysis (and more specifically the theory of singular integral
operators), and PDEs (elliptic and parabolic boundary value problems).
Once in the parabolic world, our focus will be on the striking technical differences (and
difficulties!), which make the theory ripe for further study, both from a problem solving, and
theory building perspectives.
If time permits, we will go over current, on-going, work on understanding the analogue of
graphs of Lipschitz functions, in this parabolic theory, from the point of view of its applications to PDEs

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