Alon, NogaKravitz, NoahMathematics Department2025-06-272026-09-302025-06-272026-09-302025-01-012025http://arks.princeton.edu/ark:/88435/dsp017m01bq11xhttps://theses-dissertations.princeton.edu/handle/88435/dsp017m01bq11xWe study several problems in arithmetic combinatorics, loosely grouped around the themes of "combinatorial number theory" and "higher-order Fourier analysis". The problems related to the former theme are the Lonely Runner Problem (from Diophantine approximation), questions about minimal additive complements, and a conjecture of Graham about rearrangements of subsets of F_p^\times. The problems related to the latter theme concern quantitative bounds for some instances of the Bergelson--Leibman Theorem (about subsets of N^d avoiding polynomial progressions).application/pdfenadditive combinatoricsarithmetic combinatoricscombinatoricsnumber theoryMathematicsAcademic dissertations (Ph.D.)