Abstract:
In this talk I will discuss a circle of ideas in harmonic analysis and geometric measure theory that relate the geometry of sets and measures to analytic information measured at many scales. I will explain how tools such as square functions can be used to detect geometric regularity and rectifiability, and how geometric structure can, in turn, control the behavior of these operators. The results I will present are based on joint work with John Hoffman, Tomás Merchán, Fedor Nazarov, Xavier Tolsa, and Michele Villa.
Please note the unusual time.
