February Fourier Talks 2016

Alex Iosevich

University of Rochester


Point configurations inside thin subsets of Euclidean space


We are going to explore the following basic question in geometric measure theory. How large does the Hausdorff dimension of a subset of Euclidean space need to be to ensure that it contains: i) an equilateral simplex ii) a positive proportion of all equilateral simplexes of a given dimension iii) more general geometric configurations. All the proofs involve an interplay of Fourier analytic and combinatorial methods. Connections with geometric combinatorics will also be discussed.

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