Concentration of measure on the orthogonal group and high-dimensional geometry
Elizabeth Meckes (Case Western Reserve University)
MSRI: Simons Auditorium
Many important features of the geometry of high-dimensional spaces can be seen as consequences of concentration of measure on the orthogonal group. I will illustrate this phenomenon with three examples: the Johnson-Lindenstrauss lemma, Dvoretzky's theorem, and a measure theoretic analog of the latter. The talk will be elementary and assume no prior knowledge of measure concentration or any of the results to be discussed.