Topic: harmonic analysis

Join Tom Gur’s group to study classical and quantum complexity. Research directions include sublinear algorithms, property testing, cryptography, proof systems, locally testable codes, learning theory, harmonic analysis and additive combinatorics. The one-year project connects theoretical computer science with mathematical and quantum methods.

Thomas Bloom surveys quantitative bounds for sets of integers without three-term arithmetic progressions, beginning with Roth’s zero-density theorem. Work with Olof Sisask establishes that a set with divergent reciprocal sum must contain a three-term progression, resolving the first nontrivial case of Erdős’s conjecture. The proof combines harmonic analysis with elementary combinatorics. The second part develops a structural theorem for additively non-smoothing sets: sets whose first sumset grows, while subsequent addition reveals no additional structure. Building on Bateman and Katz’s cap-se