Higher Sumsets and Energies in Additive Combinatorics and Number Theory

Abstract: We provide an overview of the results obtained by the method of higher sumsets and higher energies to some problems of additive combinatorics (the sum—product phenomenon and incidence geometry, universality, additive decomposition, etc.), number theory (exponential sums over subgroups and Gauss sums, sums with multiplicative characters, the square—root barrier), Fourier analysis (uncertainty principle) and others. We will also discuss some perspectives for this approach.

algebraic geometrynumber theory

Audience: researchers in the topic

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Number Theory Web Seminar

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