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Showing 1 to 5 of 5 for “"Arithmetic combinatorics"”.
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Topics in arithmetic combinatorics
This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L^1-norm of the Fourier transform, and the closely related idempotent theorem. The vast majority of the results regarding these problems are, in some sense, qualitative or at the very least infinitary and it …
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Two topics in arithmetic combinatorics
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms
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Additive stucture, rich lines, and exponential set-expansion
… some of the major directions of research in arithmetic combinatorics and their connections to other fields. We will then discuss three new results. The first result will generalize a structural theorem from Balog and Szemerédi. The second result will establish a new tool in incidence …
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Combinatorial aspects of synchronisation, percolation, and arithmetic
… of research in extremal, probabilistic and arithmetic combinatorics. In Chapter 2, we shall study the Kuramoto model, which is the prototypical model used for rigorous mathematical analysis in the field of synchronisation and nonlinear dynamics. A realisation of this model consists of a …
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Some arithmetic Ramsey problems and inverse theorems
In this dissertation we study arithmetic Ramsey type problems and inverse problems, in various settings. This work consists of two parts. In Part I, we study arithmetic Ramsey type problems over abelian groups. This part consists of three chapters. In Chapter 2, using hypergraph containers, we …