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Title:
The $\varepsilon^2$-conjecture of Carleson
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Abstract:
In this talk I will explain a recent result obtained in collaboration with Ben Jaye and Michele Villa where we prove the so called $\varepsilon^2$-conjecture of Carleson. This result yields a characterization (up to sets of zero length) of the tangent points of a Jordan curve in the plane in terms of the finiteness of the associated Carleson's $\varepsilon^2$-function. The proof is based on blowup methods and techniques of quantitative rectifiability.
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