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Monday, November 25, 2019 - 3:30pm

Yumeng Ou

City University of New York


University of Pennsylvania


Analysis Special Lecture

Falconer's distance set conjecture says that if a compact set $E$ in $\mathbb{R}^d$ has Hausdorff dimension larger than $d/2$, then the set of distinct distances generated by $E$ must have positive Lebesgue measure. The conjecture can be viewed as a continuous analogue of the Erdős distinct distances problem, and remains open in all dimensions. I'll discuss a variety of new tools and ideas that have recently come into play in the study of the problem, in connection with new developments in Fourier analysis, PDE, geometric measure theory, combinatorics, and beyond.